Question

you have been given three corresponding parts of two congruent triangles. using the parts, sketch a picture of the triangles, then write a congruence statement and state the theorem that proves the triangles are similar.
a. set #1: ( overline{jl} cong overline{fe}, overline{ge} cong overline{hl}, angle e cong angle l )
( \triangle jlh cong \triangle ) ? ? ? by select an answer

b. set #2: ( overline{dy} cong overline{cm}, angle y cong angle m, angle c cong angle d ):
( \triangle dyx cong \triangle ) ? ? ? by select an answer

Explanation:

Step1: Analyze Set #1

Given \(JL\cong FE\), \(GE\cong HL\), \(\angle E\cong\angle L\).
By the Side - Angle - Side (SAS) congruence theorem, if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent.
The congruence statement is \(\triangle JLH\cong\triangle FEG\)

Step2: Analyze Set #2

Given \(DY\cong CM\), \(\angle Y\cong\angle M\), \(\angle C\cong\angle D\)
By the Angle - Side - Angle (ASA) congruence theorem, if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent.
The congruence statement is \(\triangle DYX\cong\triangle CMP\)

Answer:

a. \(\triangle JLH\cong\triangle FEG\) by SAS
b. \(\triangle DYX\cong\triangle CMP\) by ASA