Question

use the figure below to answer questions 1 - 2. 1. classify by sides and angles: a) △pqr b) △qrt c) △rst

Explanation:

Step1: Recall triangle - classification rules

Triangles can be classified as equilateral (all sides equal), isosceles (two sides equal), scalene (no sides equal) by sides and as acute (all angles less than 90°), right - angled (one angle is 90°), obtuse (one angle greater than 90°) by angles.

Step2: Analyze $\triangle PQR$

In $\triangle PQR$, two sides are marked as equal. So, by sides, it is isosceles. It has a right - angle at $Q$. So, by angles, it is a right - angled triangle.

Step3: Analyze $\triangle QRT$

In $\triangle QRT$, two sides are marked as equal. So, by sides, it is isosceles. It has a right - angle at $R$. So, by angles, it is a right - angled triangle.

Step4: Analyze $\triangle RST$

In $\triangle RST$, two sides are marked as equal. So, by sides, it is isosceles. It has a right - angle at $S$. So, by angles, it is a right - angled triangle.

Answer:

a) $\triangle PQR$: Isosceles right - angled triangle
b) $\triangle QRT$: Isosceles right - angled triangle
c) $\triangle RST$: Isosceles right - angled triangle