Question

1.Which overlapping triangles are congruent by ASA?
*I meant to put F in middle of traingle*


2. Name a pair of overlapping congruent triangles in the diagram. State whether the triangles are congruent by SSS, SAS, ASA, AAS, or HL.

Answer 1

1) Which overlapping triangles are congruent by ASA?
Δ ADE and Δ EBA

ASA congruency, two angles and 1 side of a triangle is the same as the other.

2) Name a pair of overlapping congruent triangles in the diagram. State whether the triangles are congruent by SSS, SAS, ASA, AAS, or HL.

Δ HIF and Δ IHG are congruent through HL. HL only occurs in right triangles.

Answer 2

Answer:

1. Triangle EBC and triangle ADC by ASA rule of congruency

2. Triangle FIH and triangle GIH by SAS rule of congruency

Step-by-step explanation:

In figure 1,

TakingΔ EBC and ΔADC, we have

∠B=∠D (90°)

CB= CD (Given)

∠BCE=∠ACD( Common)

Therefore, by ASA rule,

Δ EBC ≅ΔADC

For figure 2, we are given that FI=GH and ∠I=∠H=90°

In ΔFIH and ΔGIH, we have

IH=IH ( Common)

∠I=∠H (90°)

FI=GH (Given)

Therefore, by SAS rule,

ΔFIH ≅ΔGIH