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Based only on the information given in the diagram, which congruence theorems or postulates could be given as reasons why HIJ KLM? Check all that apply. A. HL B. HA C. AAS D. LL E. ASA F. LA

Based only on the information given in the diagram which congruence theorems or postulates could be given as reasons why HIJ KLM Check all that

Answer :

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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