Question

4a read the following statements

1. △pqr is acute
2. △pqr is isosceles
3. △pqr is right.

which two statements contradict each other?
1 and 3
1 and 2
none of the statements contradict each other.
2 and 3

Explanation:

Step1: Define angle - type concepts

An acute - angled triangle has all angles less than 90°. A right - angled triangle has one angle equal to 90°.

Step2: Analyze contradictions

Statement 1 says $\triangle PQR$ is acute, meaning all angles are less than 90°. Statement 3 says $\triangle PQR$ is right, meaning one angle is 90°. These two statements cannot be true at the same time.

Step3: Analyze other pairs

Statement 1 (acute) and Statement 2 (isosceles) can both be true as an isosceles triangle can be acute. Statement 2 (isosceles) and Statement 3 (right) can also both be true as there are isosceles right - angled triangles.

Answer:

1 and 3