Similar Triangles and the Basic Proportionality Theorem (BPT) | Triangles | Assessment | English | Grade 10

It is given that ∆PQR ~ ∆XYZ. Which of the following statements is true? A) PQ / YZ = PR / XY B) PQ / XY = PR / XZ

• A

• B

• Both

• Neither

Answer explanation

In the two similar triangles corresponding sides are PQ and XY, QR and YZ, PR and XZ. So, PQ / XY = PR / XZ is the correct statement. Hence, the correct option is Option 2.

Tags

CCSS.HSG.SRT.A.2

In ∆ ABC, points D and E lie on sides AB and AC. It is given that DE ‖ BC, and AD / DB = 3 / 5. If AC = 4.8 cm, find AE.

• AE = 1.8 cm

• AE = 2.85 cm

• AE = 7.2 cm

Answer explanation

In ∆ ABC , DE ‖ BC, and AD / DB = 3 / 5 So as per Basic Proportionality Theorem , AD / DB = AE / EC …. ..(1) Now, AC = 4.8 cm and AC = AE + EC Let AE = x , then EC = 4.8 ─ x Putting values in Eq. 1, 3 / 5 = x / (4.8 ─ x) Cross multiplying, 3 ( 4.8 ─ x) = 5x 14.4 ─ 3 x = 5x ..... (2) 8x = 14.4 x = 1.8 cm AE = 1.8 cm So, the correct option is Option 1

Tags

CCSS.HSG.SRT.B.4

A and B are the points on sides PQ and PR respectively of ∆ PQR. PQ =20 cm, PA = 5cm, BR = 6 cm and PB = 2 cm. Is AB ‖ QR ?

• Yes

• No

• Cannot be determined

Answer explanation

In ∆ PQR , PQ =20 cm, PA = 5cm, BR = 6 cm and PB = 2 cm . So as per the converse of Basic Proportionality Theorem , AB ‖ QR if PA / AQ = PB / BR …. ..(1) Now, PQ = 20 cm and PQ = PA + AQ So AQ= 20 ─ 5 = 15 Putting values in Eq. 1, PA / AQ = 5 / 15 =1 / 3 PB / BR = 2 / 6 = 1 / 3 Hence , PA / AQ = PB / BR And so, AB ‖ QR So the correct option is Option 1

Tags

CCSS.HSG.SRT.B.4

A girl of height 90 cm is standing at the base of a shed 3.6 m high. If the length of her shadow at a certain time is 2.4 m, find the length of the shadow of the shed at the same time.

• 12m

• 9.6m

• 7.2m

• None of the above

Answer explanation

Height of girl = BD= 90cm = 0.9 m Height of shed = AB = 3.6 m AD = 3.6 ─ 0.9 = 2.7m Length of shadow of girl=BE = 2.4m EC = x Let length of shadow of shed= BC = 2.4 + x By Basic Proportionality theorem, BD/AD = BE/EC 0.9/2.7 = 2.4/EC EC = (2.7 x 2.4)/0.9 = 7.2m So length of shadow of shed= BC = 2.4 + x = 7.2 + 2.4 = 9.6m So the correct answer is Option 2

Tags

CCSS.HSG.SRT.B.4