Welcome to **AMBiPi (Amans Maths Blogs)**. In this article, you will get **51 SAT Geometry Practice Questions with Answer Keys | SAT Online Courses AMBiPi.****SAT** (Scholastic Assessment Test) is a standard test, used for taking admission to undergraduate programs of universities or colleges of United States. SAT is developed and published by the College Board, an organization in United States, administered by the Educational Testing Service.

### SAT 2022 Geometry Practice Questions

Use the diagram below to answer questions 1–5:

**SAT Geometry Question No 1:**

If the measure of angle 2 is equal to 12x + 10 and the measure of angle 8 is equal to 7x – 1, what is the measure of angle 2?

**Option A** : 9°

**Option B** : 62°

**Option C** : 108°

**Option D** : 118°

**Show/Hide Answer Key**

**Option D : 118°**

**SAT Geometry Question No 2:**

If the measure of angle 5 is five times the measure of angle 6, what is the measure of angle 5?

**Option A** : 36°

**Option B** : 120°

**Option C** : 130°

**Option D** : 150°

**Show/Hide Answer Key**

**Option D : 150°**

**SAT Geometry Question No 3:**

If the measure of angle 4 is 6x + 20 and the measure of angle 7 is 10x – 40, what is the measure of angle 6?

**Option A** : 60°

**Option B** : 70°

**Option C** : 110°

**Option D** : 120°

**Show/Hide Answer Key**

**Option C : 110°**

**SAT Geometry Question No 4:**

Which of the following is NOT true if the measure of angle 3 is 90°?

**Option A** : Angles 1 and 2 are complementary.

**Option B** : Angles 3 and 6 are supplementary.

**Option C** : Angles 5 and 7 are adjacent.

**Option D** : Angles 5 and 7 are congruent.

**Show/Hide Answer Key**

**Option A : Angles 1 and 2 are complementary.**

**SAT Geometry Question No 5:**

If the measure of angle 2 is 8x + 10 and the measure of angle 6 is x2 – 38, what is the measure of angle 8?

**Option A** : 42°

**Option B** : 74°

**Option C** : 84°

**Option D** : 108°

**Show/Hide Answer Key**

**Option A : (1 ± √29) / 4**

**SAT Geometry Question No 6:**

If the measure of angle A of triangle ABC is 3x, the measure of angle B is 5x, and the measure of angle C is 4x, what is the value of x?

**Option A** : 12°

**Option B** : 15°

**Option C** : 20°

**Option D** : 30°

**Show/Hide Answer Key**

**Option B : 15° **

**SAT Geometry Question No 7:**

If the measure of angle A of triangle ABC is 5x + 10, the measure of angle B is x + 10, and the measure of angle C is 2x, which of the following is true of triangle ABC?

**Option A** : Triangle ABC is acute but not scalene.

**Option B** : Triangle ABC is right but not isosceles.

**Option C** : Triangle ABC is obtuse but not isosceles.

**Option D** : Triangle ABC is obtuse and scalene.

**Show/Hide Answer Key**

**Option D : Triangle ABC is obtuse and scalene.**

**SAT Geometry Question No 8:**

The measure of an angle exterior to angle F of triangle DEF measures 16x + 12. If angle F measures 8x, what is the measure of angle F?

**Option A** : 7°

**Option B** : 49°

**Option C** : 56°

**Option D** : 102°

**Show/Hide Answer Key**

**Option C : 56°**

**SAT Geometry Question No 9:**

The measure of an angle exterior to angle F of triangle DEF measures 120°. Which of the following must be true?

**Option A** : Triangle DEF is acute.

**Option B** : Triangle DEF is equilateral.

**Option C** : Triangle DEF is scalene.

**Option D** : Triangle DEF is not isosceles.

**Show/Hide Answer Key**

**Option D : Triangle DEF is not isosceles.**

**SAT Geometry Question No 10:**

If the measure of angle F in triangle DEF is half the sum of the measures of angles D and E, what is the measure of an angle exterior to F?

**Option A** : 30°

**Option B** : 60°

**Option C** : 90°

**Option D** : 120°

**Show/Hide Answer Key**

**Option D : 120°**

**SAT Geometry Question No 11:**

Triangles JKL and MNO are congruent and equilateral. If side JK measures 6x + 3 and side MN measures x2 – 4, what is the length of side NO?

**Option A** : 7

**Option B** : 42

**Option C** : 45

**Option D** : 60

**Show/Hide Answer Key**

**Option C : 45**

**SAT Geometry Question No 12:**

Triangles GHI and PQR are similar and isosceles. If side HG of triangle GHI is congruent to side PQ, its corresponding side in triangle PQR, which of the following must be true?

**Option A** : Side GI is congruent to its corresponding side.

**Option B** : Angle G is congruent to angle R.

**Option C** : Angle G is congruent to angle I.

**Option D** : Side GH is congruent to side PR.

**Show/Hide Answer Key**

**Option A : Side GI is congruent to its corresponding side.**

**SAT Geometry Question No 13:**

The bases of a right triangle measure x – 3 and x + 4. If the hypotenuse of the triangle is 2x – 3, what is the length of the hypotenuse?

**Option A** : 5

**Option B** : 8

**Option C** : 12

**Option D** : 13

**Show/Hide Answer Key**

**Option D : 13**

**SAT Geometry Question No 14:**

If the length of a base of right triangle DEF is 8 units and the hypotenuse of triangle DEF is 8√5 units, what is the length of the other base?

**Option A** : 4

**Option B** : 8

**Option C** : 16

**Option D** : 32

**Show/Hide Answer Key**

**Option C : 16**

**SAT Geometry Question No 15:**

If the lengths of the bases of right triangle GHI are 9 units and 15 units respectively, what is length of the hypotenuse of triangle GHI?

**Option A** : 6√34

**Option B** : 3√34

**Option C** : 9√34

**Option D** : 8√34

**Show/Hide Answer Key**

**Option B : 3√34**

**SAT Geometry Question No 16:**

Which of the following triangles is a multiple of the triangle with sides measuring x, x – 5, and x + 5, when x is greater than 0?

**Option A** : A triangle with sides measuring 1, 2, and 3.

**Option B** : A triangle with sides measuring 3, 4, and 5.

**Option C** : A triangle with sides measuring 1, 5, and 10.

**Option D** : A triangle with sides measuring 5, 10, and 15.

**Show/Hide Answer Key**

**Option B : A triangle with sides measuring 3, 4, and 5.**

**SAT Geometry Question No 17:**

Angle T of right triangle TUV measures 45°. If base TU measures 10 units, what is the length of the hypotenuse of triangle TUV?

**Option A** : √2

**Option B** : 10√2

**Option C** : 20√2

**Option D** : 45√2

**Show/Hide Answer Key**

**Option B : 10√2**

**SAT Geometry Question No 18:**

Triangle ABC is an equilateral triangle and triangle CDE is a right triangle. If the length of side AE is 20 units, what is the length of side BD?

**Option A** : 12

**Option B** : 14

**Option C** : 16

**Option D** : 18

**Show/Hide Answer Key**

**Option B : 14**

**SAT Geometry Question No 19:**

Heather draws two regular pentagons. Which of the following is NOT always true?

**Option A** : The two regular pentagons are similar.

**Option B** : The two regular pentagons are congruent.

**Option C** : The sum of the interior angles of each pentagon is 540°.

**Option D** : The sum of the exterior angles of each pentagon is 360°.

**Show/Hide Answer Key**

**Option B : The two regular pentagons are congruent.**

**SAT Geometry Question No 20:**

The sum of the interior angles of a polygon is equal to three times the sum of its exterior angles. How many sides does the polygon have?

**Option A** : 6 sides

**Option B** : 8 sides

**Option C** : 10 sides

**Option D** : 12 sides

**Show/Hide Answer Key**

**Option B : 8 sides**

**SAT Geometry Question No 21:**

Andrea draws a polygon with x number of sides. The sum of the interior angles of her polygon is 60 times its number of sides. How many sides does Andrea’s polygon have?

**Option A** : 3 sides

**Option B** : 4 sides

**Option C** : 5 sides

**Option D** : 6 sides

**Show/Hide Answer Key**

**Option A : 3 sides**

**SAT Geometry Question No 22:**

If the sum of the interior angles of a polygon is equal to the sum of the exterior angles, which of the following statements must be true?

**Option A** : The polygon is a regular polygon.

**Option B** : The polygon has 4 sides.

**Option C** : The polygon has 6 sides.

**Option D** : It is impossible for these sums to be equal.

**Show/Hide Answer Key**

**Option C : The polygon has 6 sides.**

**SAT Geometry Question No 23:**

The sum of the interior angles of a polygon is 9x^{2}. If x is 3 greater than the number of sides of the polygon, how many sides does the polygon have?

**Option A** : 6 sides

**Option B** : 7 sides

**Option C** : 10 sides

**Option D** : 12 sides

**Show/Hide Answer Key**

**Option B : 7 sides**

**SAT Geometry Question No 24:**

Pentagons ABCDE and FGHIJ are similar. The ratio of each side of pentagon ABCDE to its corresponding side of pentagon FGHIJ is 4:1. If AB and FG are corresponding sides, and the length of AB is 4x + 4, what is the length of FG?

**Option A** : x + 1

**Option B** : 2(x + 1)

**Option C** : 4(x + 1)

**Option D** : 8(x + 1)

**Show/Hide Answer Key**

**Option A : x + 1**

**SAT Geometry Question No 25:**

Andrew constructs a polygon with four sides and no right angles. His polygon

**Option A** : could be a parallelogram, but cannot be a rectangle.

**Option B** : could be a rhombus, but cannot be a parallelogram.

**Option C** : could be a rectangle, but cannot be a square.

**Option D** : could be a parallelogram or a rectangle, but not a square.

**Show/Hide Answer Key**

**Option A : could be a parallelogram, but cannot be a rectangle.**

**SAT Geometry Question No 26:**

Angle E of rhombus EFGH measures 3x + 5. If the measure of angle H is 4x, what is the measure of angle F?

**Option A** : 20°

**Option B** : 80°

**Option C** : 100°

**Option D** : 120°

**Show/Hide Answer Key**

**Option C : 100°**

**SAT Geometry Question No 27:**

DeDe has four identical line segments. Using them, she can form

**Option A** : a rhombus, but not a parallelogram.

**Option B** : a square or a rectangle, but not a parallelogram.

**Option C** : a square, but not a rhombus or a rectangle.

**Option D** : a square, rhombus, rectangle, or parallelogram.

**Show/Hide Answer Key**

**Option D : a square, rhombus, rectangle, or parallelogram.**

**SAT Geometry Question No 28:**

The diagonals of rectangle ABCD intersect at E. Which of the following is NOT always true?

**Option A** : angle AEB = angle DEC

**Option B** : angle EDC = angle EBA

**Option C** : angle DAE = angle EDA

**Option D** : angle DCE = angle ECB

**Show/Hide Answer Key**

**Option D : angle DCE = angle ECB**

**SAT Geometry Question No 29:**

Monica draws a quadrilateral whose diagonals form four right triangles inside the quadrilateral. This quadrilateral

**Option A** : must have four congruent angles.

**Option B** : must have four congruent sides.

**Option C** : must have congruent diagonals.

**Option D** : must be a square.

**Show/Hide Answer Key**

**Option B : must have four congruent sides.**

**SAT Geometry Question No 30:**

Four squares are joined together to form one large square. If the perimeter of one of the original squares was 8x units, what is the perimeter of the new, larger square?

**Option A** : 16x units

**Option B** : 20x units

**Option C** : 24x units

**Option D** : 32x units

**Show/Hide Answer Key**

**Option A : 16x units**

**SAT Geometry Question No 31:**

If the height of a triangle is half its base, b, what is the area of the triangle?

**Option A** : b/4

**Option B** : b^{2}/4

**Option C** : b/2

**Option D** : b^{2}/2

**Show/Hide Answer Key**

**Option B : b ^{2}/4**

**SAT Geometry Question No 32:**

Triangle DEC is inscribed in rectangle ABCD. If side AB = 30 units, side EC = 17 units, and side AE = side EB, what is the area of triangle DEC?

**Option A** : 60 square units

**Option B** : 120 square units

**Option C** : 136 square units

**Option D** : 240 square units

**Show/Hide Answer Key**

**Option B : 120 square units**

**SAT Geometry Question No 33:**

The area of a rectangle is x2 + 7x + 10 square units. If the length of the rectangle is x + 2 units, what is the width of the rectangle?

**Option A** : x + 2

**Option B** : x + 4

**Option C** : x + 5

**Option D** : 2x + 4

**Show/Hide Answer Key**

**Option C : x + 5**

**SAT Geometry Question No 34:**

If the lengths of the sides of a square are halved, the area of the new square is

**Option A** : one-fourth the area of the old square

**Option B** : one-half the area of the old square

**Option C** : equal to the area of the old square.

**Option D** : four times the area of the old square.

**Show/Hide Answer Key**

**Option A : one-fourth the area of the old square**

**SAT Geometry Question No 35:**

The perimeter of a square is 3x – 4 units. If the area of the square is 25 square units, what is the value of x?

**Option A** : 5

**Option B** : 6

**Option C** : 7

**Option D** : 8

**Show/Hide Answer Key**

**Option D : 8**

**SAT Geometry Question No 36:**

The length of a rectangle is two less than three times its width. If the area of the rectangle is 96 cm^{2}, what is the length of the rectangle?

**Option A** : 6

**Option B** : 8

**Option C** : 16

**Option D** : 18

**Show/Hide Answer Key**

**Option C : 16**

**SAT Geometry Question No 37:**

A cylinder has a volume of 45π in^{3}. Which of the following could be the radius and height of the cylinder?

**Option A** : radius = 3 in., height = 5 in.

**Option B** : radius = 3 in., height = 15 in.

**Option C** : radius = 5 in., height = 3 in

**Option D** : radius = 9 in., height = 5 in.

**Show/Hide Answer Key**

**Option A : radius = 3 in., height = 5 in.**

Use the diagram below to answer questions 38 to 42. The diagram is not to scale.

**SAT Geometry Question No 38:**

If the length of AO is 15 units, what is the circumference of the circle?

**Option A** : 15π units

**Option B** : 30 units

**Option C** : 30π units

**Option D** : 225 units

**Show/Hide Answer Key**

**Option C : 30π units**

**SAT Geometry Question No 39:**

If the measure of angle AOC is 60°, what is the measure of arc DB?

**Option A** : 30°

**Option B** : 60°

**Option C** : 120°

**Option D** : 300°

**Show/Hide Answer Key**

**Option B : 60°**

**SAT Geometry Question No 40:**

If the length of OD is 6 units and the measure of angle COB is 100°, what is the length of arc CB?

**Option A** : 10π/3 units

**Option B** : 12π units

**Option C** : 50π/3 units

**Option D** : 600π units

**Show/Hide Answer Key**

**Option A : 10π/3 units**

**SAT Geometry Question No 41:**

If the area of the circle is 196π square units, what is the length of CD?

**Option A** : 7 units

**Option B** : 14 units

**Option C** : 28 units

**Option D** : 56 units

**Show/Hide Answer Key**

**Option C : 28 units**

**SAT Geometry Question No 42:**

If the length of OA is 8 units and the measure of angle AOC is 50°, what is the area of sector AOC?

**Option A** : 5π/18 units

**Option B** : 10π/9 units

**Option C** : 32π/25 units

**Option D** : 80π/9 units

**Show/Hide Answer Key**

**Option D : 80π/9 units**

**SAT Geometry Question No 43:**

The endpoints of a line segment are (–3,6) and (7,4). What is the slope of this line?

**Option A** : -5

**Option B** : -1/5

**Option C** : 1/5

**Option D** : 5

**Show/Hide Answer Key**

**Option B : -1/5**

**SAT Geometry Question No 44:**

The endpoints of a line segment are (5,–5) and (–5,–5). What is the slope of this line?

**Option A** : -10

**Option B** : -15

**Option C** : 0

**Option D** : 10

**Show/Hide Answer Key**

**Option C : 0**

**SAT Geometry Question No 45:**

What is the slope of a line segment with endpoints at (–1,2) and (1,10)?

**Option A** : -4

**Option B** : -1/4

**Option C** : 4

**Option D** : 1/4

**Show/Hide Answer Key**

**Option C : 4**

**SAT Geometry Question No 46:**

What is the midpoint of a line segment with endpoints at (0,–8) and (–8,0)?

**Option A** : (–8,–8)

**Option B** : (–4,–4)

**Option C** : (–1,–1)

**Option D** : (4, 4)

**Show/Hide Answer Key**

**Option B : (-4, -4)**

**SAT Geometry Question No 47:**

What is the midpoint of a line segment with endpoints at (6,–4) and (15,8)?

**Option A** : (9, 4)

**Option B** : (9, 8)

**Option C** : (10.5, 2)

**Option D** : (12, 2)

**Show/Hide Answer Key**

**Option C : (10.5, 2)**

**SAT Geometry Question No 48:**

The endpoints of a line segment are (0,–4) and (0,4). What is the midpoint of this line?

**Option A** : (0, 0)

**Option B** : (0, -2)

**Option C** : (0, 2)

**Option D** : (-4, 4)

**Show/Hide Answer Key**

**Option A : (0, 0)**

**SAT Geometry Question No 49:**

What is the distance from the point (–6,2) to the point (2,17)?

**Option A** : 18 units

**Option B** : 17 units

**Option C** : 16 units

**Option D** : 23 units

**Show/Hide Answer Key**

**Option B : 17 units**

**SAT Geometry Question No 50:**

Which of the following is the product of the slopes of perpendicular lines?

**Option A** : -1

**Option B** : -1/2

**Option C** : 0

**Option D** : 1/3

**Show/Hide Answer Key**

**Option A : -1**

**SAT Geometry Question No 51:**

Line A is perpendicular to line B. If the slope of line A is multiplied by 4, what must the slope of line B be multiplied by in order for the lines to still be perpendicular?

**Option A** : 1/4

**Option B** : -1/4

**Option C** : 4

**Option D** : -4

**Show/Hide Answer Key**

**Option A : 1/4**