Question

Determine if the triangles are congruent. If so, write a congruence statement. Explain your reasoning in a short paragraph proof.
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Answer 1

Answer: Yes

Step-by-step explanation:

The Vertical angle would show that 2 of the angles are exactly the same. Its also given 2 lines that are marked as congurent. Since we know that angle and the lines are congruent we can also say that angle IFJ is congruent to angle IHG meaning that they are congruent because of ASA (Angle Side Angle Theorem)

Answer 2

Congruent triangles have equal corresponding sides lengths and angle measures.

The triangles are congruent by ASA

From the attached figure, we have:

$\mathbf{HI \cong IF}$

Lines HG and JF are parallel lines.

It means that:

Angles G and F are corresponding, and also angles at I in both triangles are vertical angles.

So, we can conclude that both triangles are congruent by ASA

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