Question

for each figure below, determine (by using the markings) if there is a pair of congruent triangles, state the congruence and give the property justifying the congruence.
note that the pairs of triangles are drawn as congruent, but you should not rely on how they are drawn for your answers.
if necessary, you may learn what the markings on a figure indicate.
(a)
$\triangle ghi cong \triangle\boldsymbol{\square}$ by the
$\bigcirc$ not necessarily congruent
$\bigcirc$ congruent:
(b)
$\triangle mno cong \triangle\boldsymbol{\square}$
$\bigcirc$ not necessarily congruent
$\bigcirc$ congruent:

Explanation:

Step1: Analyze triangle pair (a)

In $\triangle GHI$ and $\triangle KJL$:

• $\overline{HI} = \overline{KL}$ (marked congruent side)
• $\angle H = \angle L$ (marked congruent angle)
• $\angle I = \angle K$ (marked congruent angle)

This matches the AAS (Angle-Angle-Side) congruence criterion, with the correspondence $\triangle GHI \cong \triangle JLK$.

Step2: Analyze triangle pair (b)

In $\triangle MNO$ and $\triangle PQR$:

• $\angle M = \angle Q$ (marked congruent angle)
• $\angle O = \angle R$ (marked congruent angle)
• $\overline{NO}

eq \overline{QR}$ (only $\overline{QR}$ has a congruence mark, no matching mark on $\triangle MNO$)
No valid congruence criterion is satisfied, so the triangles are not necessarily congruent.

Step3: Analyze triangle pair (c)

The only markings are a single congruent side on each triangle, with no congruent angles or additional congruent sides. No congruence criterion can be applied, so the triangles are not necessarily congruent.

Answer:

(a) Congruent: $\triangle GHI \cong \triangle JLK$ by the AAS (Angle-Angle-Side) congruence criterion
(b) Not Necessarily Congruent
(c) Not Necessarily Congruent