Which of the following pairs of triangles is congruent by ASA?(1 point)

Question

Responses

Two congruent triangles, upper A upper B upper C and upper Q upper R upper S are shown within an 11 column by 5 row grid.
Image with alt text: Two congruent triangles, upper A upper B upper C and upper Q upper R upper S are shown within an 11 column by 5 row grid.

Two right triangles, upper L upper N upper M and upper X upper Y upper Z are shown within a 7 column by 5 row grid as mirror images of each other.
Image with alt text: Two right triangles, upper L upper N upper M and upper X upper Y upper Z are shown within a 7 column by 5 row grid as mirror images of each other.

Two congruent triangles, upper A upper B upper C and upper Q upper R upper S are shown within an 11 columns by 5 row grid.
Image with alt text: Two congruent triangles, upper A upper B upper C and upper Q upper R upper S are shown within an 11 columns by 5 row grid.

A vertically oriented kite shape upper G upper H upper I upper J is bisected by a vertical line from upper G to upper I, dividing the kite into two equal triangles upper G upper H upper I and upper G upper J upper I. Angles are labeled.

Answer 1

To determine which pairs of triangles are congruent by the ASA (Angle-Side-Angle) postulate, we need to look for pairs of triangles that have two angles and the included side congruent.

From your description:

1. The congruent triangles \( \triangle ABC \) and \( \triangle QRS \): Since these triangles are stated to be congruent, they satisfy the congruence criteria, but we need to analyze the congruence condition established by the ASA postulate specifically.

2. The right triangles \( \triangle LNM \) and \( \triangle XYZ \): As mirror images (but which could suggest they maintain congruent angle relationships with their sides), we would need to confirm they indeed have one angle from the first triangle which corresponds to an angle from the second triangle with the included side between those angles being equal.

3. The congruent triangles again mentioned \( \triangle ABC \) and \( \triangle QRS \): This is a repeat of the first item, and reinforces their congruence.

4. The kite shape where triangles \( \triangle GHI \) and \( \triangle GJI \) are created: Because the kite is symmetric and the common side \( GI \) lies between angles \( GHI \) and \( GJI \), this implies they meet ASA criterion as the angles at \( G \) and the angles \( H \) and \( J \) will be equal due to symmetry.

Conclusion:

• The pairs of triangles that can potentially be congruent by ASA would most likely be the triangles formed from the kite shape if angles \( GHI \) and \( GJI \) were congruent, along with the common side \( GI \).

If applying the strict ASA analysis, the most definitive answer would likely rely on the specifics of angle measurements provided for those triangles. If both angles at vertex \( G \) are equal, along with side \( GI \) being included between them, then the pair of triangles from the kite, \( \triangle GHI \) and \( \triangle GJI \) could be congruent by ASA.

If you provide angle measures or a diagram, more precise conclusions could be made.