The congruency postulates or theorem that could be given as reasons why ΔHIJ ≅ ΔKLM are;
B. HA
C. AAS
What makes two triangles congruent?
Two triangles are congruent is they satisfy one of the congruency theorems which includes;
- AAS; Angle-angle-Side congruency postulate
- ASA; Angle-Side-Angle congruency postulate
- SAS; Side-Angle-Side congruency postulate
- SSS; Side-Side-Side congruency postulate
- HL; Hypotenuse length congruency theorem
- HA; Hypotenuse angle congruency theorem
The information in the diagram of the question are;
Angle ∠IHJ in triangle ΔHIJ is congruent to a angle ∠LKM in ΔKLM
Angle ∠IJH in triangle ΔHIJ is congruent to angle ∠LMK in triangle ΔKLM
Segment [tex]\overline{IJ}[/tex] in triangle ΔHIJ is congruent to [tex]\overline{LM}[/tex] in triangle ΔKLM
The information in the question can be described as follows;
Two adjacent angles and a non included angle in triangle ΔIJH are congruent to two angles and the non included side in ΔKLM
Therefore;
- Triangle ΔHIJ is congruent to triangle ΔKLM by Angle-Angle-Side, AAS congruency postulate
Angle ∠IHJ in triangle ΔHIJ = 90° and angle ∠LKM in triangle ΔKLM = 90°
Therefore, triangle ΔHIJ and triangle ΔKLM are right triangles
The hypotenuse side in triangle ΔHIJ is congruent to the hypotenuse side of ΔKLM
From the diagram, angle ∠IJK is congruent to angle ∠LMK, therefore;
- Triangle ΔHIJ is congruent to ΔKLM by Hypotenuse-Angle, HA congruency postulate
Hypotenuse Angle, HA, congruency theorem states that two triangles are congruent if the hypotenuse side and the acute angle of one right triangle are congruent the hypotenuse side and one acute angle of the other right triangle
The correct options are; B. HA, and C. AAS
Learn more about the rules of congruency between triangles here:
https://brainly.com/question/1675117
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