Question

is δpqr similar to δxyz? options: yes, no

Explanation:

Step1: Determine coordinates of vertices

For \( \triangle XYZ \): Let's assume grid units. Let \( X=(3,4) \), \( Y=(3,8) \), \( Z=(6,8) \). So \( XY = 8 - 4 = 4 \) (vertical), \( YZ = 6 - 3 = 3 \) (horizontal), \( XZ \) can be found by distance formula \( \sqrt{(6 - 3)^2+(8 - 4)^2}=\sqrt{9 + 16}=5 \).

For \( \triangle PQR \): Let \( P=(3, -1) \), \( Q=(5, -1) \), \( R=(5, -3) \). So \( PQ = 5 - 3 = 2 \) (horizontal), \( QR = -1 - (-3)=2 \) (vertical), \( PR \) distance \( \sqrt{(5 - 3)^2+(-3 + 1)^2}=\sqrt{4 + 4}=\sqrt{8}=2\sqrt{2} \).

Step2: Check similarity ratios

For \( \triangle XYZ \), sides are \( 3,4,5 \) (ratio \( 3:4:5 \)). For \( \triangle PQR \), sides are \( 2,2,2\sqrt{2} \) (ratio \( 1:1:\sqrt{2} \), isosceles right triangle). The ratios of corresponding sides are not equal (\( \frac{3}{2}
eq\frac{4}{2}\)), so angles won't be equal. Thus, not similar.

Answer:

No