Question

iii. state whether each pair of triangles is congruent by sss, sas, asa, aas, hl, or none.

Explanation:

Step1: Recall congruence postulates

SSS (Side - Side - Side): All three sides of one triangle are equal to the corresponding sides of the other triangle. SAS (Side - Angle - Side): Two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of the other triangle. ASA (Angle - Side - Angle): Two angles and the included side of one triangle are equal to the corresponding two angles and included side of the other triangle. AAS (Angle - Angle - Side): Two angles and a non - included side of one triangle are equal to the corresponding two angles and non - included side of the other triangle. HL (Hypotenuse - Leg): For right - angled triangles, the hypotenuse and one leg of one right - angled triangle are equal to the hypotenuse and one leg of the other right - angled triangle.

Step2: Analyze each pair of triangles

For each pair, identify the marked equal sides and angles. Match the given equal parts with the congruence postulates. For example, if two sides and the included angle are marked equal, it is SAS; if all three sides are marked equal, it is SSS.
(As there are 30 pairs, we will not analyze each one in detail here. But the general process is as above.)

Since we are not given specific details about each pair in text (only the image), we can't provide a detailed answer for each pair. But the general way to answer for each pair would be:

1. Identify the marked equal sides and angles in the pair of triangles.
2. Match with the congruence postulate (SSS, SAS, ASA, AAS, HL) or conclude it is none if no postulate is satisfied.

Answer:

Without specific analysis of each pair from the image, we can't give a definite answer for each of the 30 pairs. The general method to find the answer for each pair is as described in the explanation.