Question

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Explanation:

Part (a)

Step1: Recall HL Congruence

HL (Hypotenuse - Leg) Congruence applies to right - angled triangles. It states that if the hypotenuse and one leg of a right - triangle are equal to the hypotenuse and one leg of another right - triangle, then the two right - triangles are congruent.
In part (a), we have two right - triangles. The length of one leg is 12 km for both triangles, and the length of the hypotenuse is 20 km for both triangles. So, the hypotenuse and one leg of the first right - triangle are equal to the hypotenuse and one leg of the second right - triangle.

Step2: Determine the answer

Since the conditions for HL Congruence are met (right - triangles, equal hypotenuse, equal leg), the HL Congruence property can be used.

Step1: Recall HL Congruence

HL Congruence is for right - angled triangles. We need to check if we have information about hypotenuse and leg. In the two triangles in part (b), we have some marked sides, but we need to see if we can identify hypotenuse and leg. The markings show some equal sides, but we don't have clear identification of hypotenuse (the side opposite the right angle) and a leg for HL. Also, we need to ensure that the triangles are right - angled and we have hypotenuse - leg correspondence. In this case, the markings do not clearly give us a hypotenuse and a leg that are equal between the two triangles in a way that satisfies HL.

Step2: Determine the answer

Since the conditions for HL (having a hypotenuse and a leg equal between two right - triangles) are not met, the HL Congruence property cannot be used.

Step1: Recall HL Congruence

HL Congruence is applicable only to right - angled triangles. The triangle in part (c) is not a right - angled triangle (there is no right - angle mark). HL Congruence property is for right - triangles, so for non - right - triangles, HL cannot be used.

Step2: Determine the answer

Since the triangles are not right - angled, the HL Congruence property cannot be used.

Answer:

Yes

Part (b)