Question

drag the triangle pairs into the correct columns. drag a drop the answer congruent triangle pairs non - congruent triangle pairs not drawn to scale

Explanation:

Step1: Recall congruent - triangle criteria

Two triangles are congruent if they have the same shape and size. This can be determined by SSS (Side - Side - Side), SAS (Side - Angle - Side), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side), and HL (Hypotenuse - Leg for right - triangles).

Step2: Analyze the first pair

The first pair is a translation of one triangle to get the other. Translations are rigid motions that preserve shape and size. So, this pair is congruent.

Step3: Analyze the second pair

The second pair has two triangles with two pairs of corresponding sides equal and the included angles equal (SAS criterion). So, this pair is congruent.

Step4: Analyze the third pair

The third pair shows a dilation. Dilation changes the size of the triangle. So, this pair is non - congruent.

Step5: Analyze the fourth pair

The fourth pair does not satisfy any of the congruence criteria. The side and angle markings do not match up in a way to show congruence. So, this pair is non - congruent.

Answer:

Congruent Triangle Pairs: First pair, Second pair
Non - Congruent Triangle Pairs: Third pair, Fourth pair