Question

1. here is a pair of congruent triangles. which congruence condition is satisfied?

7cm
19cm
7cm
19cm
diagram not to scale
○ asa
○ sas
○ sss
○ rhs

Explanation:

Step1: Identify triangle type

Both triangles are right - angled (have a right angle, indicated by the square corner).

Step2: Analyze given sides

In a right - angled triangle, the hypotenuse is the longest side. Here, both triangles have a side of length 7 cm (one leg), a hypotenuse of length 19 cm, and a right angle. The RHS (Right - angled, Hypotenuse, Side) congruence criterion states that if the hypotenuse and one leg of a right - angled triangle are equal to the hypotenuse and one leg of another right - angled triangle, then the two triangles are congruent. The two triangles have a right angle, the hypotenuse (19 cm) is equal, and one leg (7 cm) is equal. So the congruence condition satisfied is RHS. Also, let's check other criteria:

• ASA: Requires two angles and the included side. We don't have information about two angles here, so not ASA.
• SAS: Requires two sides and the included angle. The included angle for the two sides (7 cm and the other leg) would be the right angle, but we also have the hypotenuse. But RHS is more specific for right - angled triangles.
• SSS: Requires all three sides to be equal. We only know two sides (7 cm and 19 cm), we don't know about the third leg (we can calculate it using Pythagoras, but we are not given it, and RHS is a better fit as we know hypotenuse and one leg).

Answer:

D. RHS