**SSC CGL Geometry Similar Triangles Set 1 : Ques No 1**

In triangle ABC, two points D and E are taken on the lines AB and BC respectively in such a way that AC is parallel to DE. The triangles ABC and DBE are

**Options:**

A. always similar

B. always congruent

C. similar only if D lies outside the line segment AB

D. congruent only if D lies outside the line segment AB

**Answer: **

**Solution:**

**SSC CGL Geometry Similar Triangles Set 1 : Ques No 2**

In a right triangle ABC, the angle A = 90 degree and AD is perpendicular to BC. If areas of the triangles ABC and ACD are 40 cm^{2} and 10 cm^{2} respectively and AC = 9 cm, then the length of BC is

**Options:**

A. 4 cm

B. 12 cm

C. 18 cm

D. 6 cm

**Answer: **

**Solution: **

**SSC CGL Geometry Similar Triangles Set 1 : Ques No 3**

In a triangle ABC, D and E are two points on the sides AC and BC respectively, such that DE = 18 cm, CE = 5 cm and the angle DEC = 90 degree. If tan(∠ABC) = 3.6, then AD : CD is equal to

**Options:**

A. 2BC : CE

B. BC : 2CE

C. CE : 2BC

D. 2CE : BC

**Answer: B**

**Solution:**

**SSC CGL Geometry Similar Triangles Set 1 : Ques No 4**

In a triangle ABC, when the points D and E on sides AB and AC are joined, the line DE turns out to be parallel to BC and also bisects the triangle into two equal areas. The ratio of DB : AB is

**Options:**

A. 1 : 2

B. √2 : 1

C. (√2 – 1) : √2

D. 1 : √2

**Answer: C**

**Solution:**

**SSC CGL Geometry Similar Triangles Set 1 : Ques No 5**

Two similar triangles have the areas 96 cm^{2} and 150 cm^{2}. If the largest side of the larger triangle is 20 cm, the largest side of the smaller triangle (in cm) is

**Options:**

A. 20

B. 15

C. 16

D. 18

**Answer: C**

**Solution:**

**SSC CGL Geometry Similar Triangles Set 1 : Ques No 6**

The perimeter of similar triangles ABC and PQR are 24 cm and 36 cm respectively. If AB = 10 cm, then PQ (in cm) is

**Options:**

A. 18

B. 12

C. 15

D. 16

**Answer: C**

**Solution:**

**SSC CGL Geometry Similar Triangles Set 1 : Ques No 7**

In triangle ABC, the bisector of angle A is AP and it meets BC at P. If a line DE intersects AB, AP and AC at D, Q and E respectively and is perpendicular to AP, then which of the following is true?

**Options:**

A. AQ = QP

B. AD = AE

C. BP = PC

D. QP = EC

**Answer: B**

**Solution:**

**SSC CGL Geometry Similar Triangles Set 1 : Ques No 8**

In triangle ABC, DE || BC and AD : DB = 5 : 4. Then the ratio DE : BC is

**Options:**

A. 4 : 5

B. 9 : 5

C. 5 : 9

D. 4 : 9

**Answer: C**

**Solution:**

**SSC CGL Geometry Similar Triangles Set 1 : Ques No 9**

In a triangle ABC, BC = 12 cm. A line CD is drawn to intersect AB at D internally. If DB = 9 cm, CD = 6 cm and ∠BCD = ∠BAC, the ratio of the perimeter of ∆ADC to that of ∆BDC is

**Options:**

A. 5/9

B. 2/3

C. 7/9

D. 8/9

**Answer: C**

**Solution: **

**SSC CGL Geometry Similar Triangles Set 1 : Ques No 10**

In a triangle ABC, the line BB_{1} through B intersects side AC at B_{1}. A line through A parallel to BB_{1}, meets CB extended at A_{1} and another line through C parallel to BB_{1} meets AB extended at C_{1}. Then, which of the following is true?

**Options:**

A. 1/AA_{1} – 1/CC_{1} = 2/BB_{1}

B. 1/BB_{1} – 1/AA_{1} = 2/CC_{1}

C. 1/CC_{1} + 1/AA_{1} = 1/BB_{1}

D. 1/CC_{1} – 1/AA_{1} = 1/BB_{1}

**Answer: C**

**Solution:**

**SSC CGL Geometry Similar Triangles Set 1 : Ques No 11**

AD is perpendicular to the internal bisector of ∠ABC of ∆ABC. DE is drawn through C and parallel to BC to meet AC at E. If the length of AC is 12 cm, then the length of AE (in cm) is

**Options:**

A. 3

B. 4

C. 6

D. 8

**Answer: C**

**Solution:**