Question

which of the following pairs of triangles could be proven by sas congruence theorem? (1 point)

Explanation:

Step1: Recall SAS Congruence Theorem

The SAS (Side - Angle - Side) Congruence Theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Step2: Analyze the first pair

In the first pair of triangles $\triangle ABC$ and $\triangle QRS$, we need to check if two sides and the included - angle are congruent. By observing the grid, we can count the lengths of the sides and check the angles. If we assume the grid squares have side - length 1, we can use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ to find side lengths. Also, we need to check if the angles between the corresponding sides are equal. After analysis, we find that the first pair does not satisfy SAS.

Step3: Analyze the second pair

In the second pair of triangles $\triangle XYZ$ and $\triangle ABC$, we check the side - lengths and included angles. By counting the grid units for side - lengths and observing the angles, we can see that two sides and the included angle of $\triangle XYZ$ are congruent to two sides and the included angle of $\triangle ABC$. For example, we can find the lengths of the sides using the grid and see that the marked angles are equal.

Answer:

The second pair of triangles (the pair with $\triangle XYZ$ and $\triangle ABC$) can be proven congruent by the SAS Congruence Theorem.