Question

Complete the statements to verify that the triangles are similar.

StartFraction Q R Over T U EndFraction = A.1/4 B.1/2 C.2 D.4


StartFraction P R Over S U EndFraction = A.1/2 B.2 C.4 D.6


StartFraction P Q Over S T EndFraction = StartFraction StartRoot 52 EndRoot Over StartRoot 13 EndRoot EndFraction = A.1/2 B.2 C.4 D.6


Therefore, △PQR ~ △STU by_________ the theorem. A.SAS congruency B.SAS similarity C.SSS congruency D.SSS similarity

Answer 1

did on edge

Explanation:

Answer 2

1. Option C

2. Option B

3. Option B

4. Option D

Explanation:

From the given graph it is clear that

PR = 6 units

QR = 4 units

TU = 2 units

SU = 3 units

Now,

`(QR)/(TU)=(4)/(2)=2`

Hence, the correct option is C.

`(PR)/(SU)=(6)/(3)=2`

Hence, the correct option is B.

Using given information, we get

`(PQ)/(ST)=(√(52))/(√(13))=(√(4* 13))/(√(13))=(2√(13))/(√(13))=2`

Hence, the correct option is B.

We conclude that all corresponding sides are proportional.

`(QR)/(TU)=(PR)/(SU)=(PQ)/(ST)=2`

`\therefore \Delta PQR\sim \Delta STU` (Using SSS similarity)

Hence, the correct option is D.