Question

triangles jgh and klm are shown.
gj = 8.1, jh = 6.6, lk = 8.1 and km = 6.6
two students examine the figures. sarah claims that the two triangles can be proven congruent by the sas (side - angle - side) triangle congruence theorem. joseph claims that the two triangles can be proven congruent by the sas (side - angle - side) triangle similarity theorem.
using the dropdown below to complete the sentence.
select correct because
select

Explanation:

Step1: Recall triangle congruence and similarity theorems

The SAS (side - angle - side) triangle congruence theorem states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent. The SAS (side - angle - side) triangle similarity theorem states that if two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, then the two triangles are similar.

Step2: Analyze the given side lengths and angles

We are given \(GJ = LK=8.1\), \(JH = KM = 6.6\), and the included angles \(\angle J=\angle K = 55^{\circ}\). Since the side lengths are equal (\(GJ = LK\), \(JH = KM\)) and the included angles are equal (\(\angle J=\angle K\)), we use the congruence theorem.

Answer:

Sarah is correct because two sides and the included angle of \(\triangle GJH\) are equal to two sides and the included angle of \(\triangle LKM\) (by the SAS triangle congruence theorem).