Question

Two similar triangles are shown below:

Two triangles are shown. The sides of the triangle on the left are marked 6, 8, 4. The sides of the triangle on the right are marked as 3, 4, and 2. For the triangle on the left, the angle between sides marked 8 and 6 is labeled as p, marked by a double arc, and the angle between the sides marked 8 and 4 is labeled as q, marked by a single arc. The third angle is marked by a triple arc. For the triangle on the right, the angle between sides marked 2 and 4 is labeled as r and the angle between the sides marked 4 and 3 is labeled as s, marked by a double arc. The angle between the sides 2 and 3 is labeled as t, marked by a triple arc and it is also the angle on the top vertex of this triangle.

Which two sets of angles are corresponding angles?

∠p and ∠r; ∠q and ∠s
∠p and ∠s; ∠q and ∠r
∠p and ∠t; ∠q and ∠s
∠p and ∠t; ∠q and ∠r

Answer 1

<p and <s; <q and <r is the answer

Answer 2

Let name the two triangles as ΔABC and ΔP QR.

Length of corresponding sides of two triangles are proportional.

`(QR)/(AB)=(PR)/(AC)=(PQ)/(BC)\\\\(4)/(8)=(3)/(6)=(2)/(4)=(1)/(2)`

So, by Side-Side-Side , Similarity Axiom of two triangles

ΔBAC~ ΔQRP →[SSS]

The two sets of angles which are corresponding angles

Option B: ∠p and ∠s; ∠q and ∠r

The reason being that if two triangles are similar ,their corresponding angles are equal.