Question

determine the congruent criteria that can be used to prove each pair of triangles is congruent or not.
definition of ≅ △s
side - side - side (sss)
side - angle - side sas
angle - angle - side (aas)
angle - side - angle (asa)
hypotenuse - leg (hl)
definition of ≅ △s
side - side - side (sss)
side - angle - side sas
angle - angle - side (aas)
angle - side - angle (asa)
hypotenuse - leg (hl)
definition of ≅ △s
side - side - side (sss)
side - angle - side sas
angle - angle - side (aas)
angle - side - angle (asa)
hypotenuse - leg (hl)
definition of ≅ △s
side - side - side (sss)
side - angle - side sas
angle - angle - side (aas)
angle - side - angle (asa)
hypotenuse - leg (hl)

Explanation:

Step1: Analyze the first pair of triangles

Check the given sides and angles. The first pair has two sides equal (marked with one tick and side length \(4\) units). But no information about included angles.

Step2: Analyze the second pair of triangles

One triangle has a side - angle - side (two sides with one common angle). But the other triangle's angle is not the included angle.

Step3: Analyze the third pair (right - angled triangles)

Both are right - angled, hypotenuse (\(5\) cm) and one leg (equal as per markings) are equal. So, by Hypotenuse - Leg (HL) criterion.

Step4: Analyze the fourth pair

Two sides are equal (marked with two ticks and side length \(8\) cm). So, by Side - Side - Side (SSS) criterion.

Step5: Analyze the fifth pair

Two angles and a non - included side. So, by Angle - Angle - Side (AAS) criterion.

Step6: Analyze the sixth pair

Only one angle and one side marked. Not sufficient to prove congruence.

Answer:

1. No congruence criterion (not enough information).
2. No congruence criterion (not correct angle - side - angle).
3. Hypotenuse - Leg (HL).
4. Side - Side - Side (SSS).
5. Angle - Angle - Side (AAS).
6. No congruence criterion (not enough information).