Question

select the correct answer from each drop - down menu. consider triangles abc and qpr shown. triangle abc is dropdown triangle qpr. since the transformations dropdown, the triangles are dropdown. reset next

Explanation:

Step1: Analyze Triangle ABC

In triangle \(ABC\), side \(AC\) has two marks (indicating a certain length), side \(BC\) has one mark, and angle at \(C\) is considered.

Step2: Analyze Triangle QPR

In triangle \(QPR\), side \(QR\) has two marks, side \(PR\) has one mark, and angle at \(R\) is considered.

Step3: Check Congruence Conditions

We can see that there is a pair of equal sides (the ones with one mark), a pair of equal sides (the ones with two marks), and the included angles (at \(C\) and \(R\)) are equal (since the triangles are oriented such that the angle between the sides with one and two marks is the included angle). By the SAS (Side - Angle - Side) congruence criterion, triangle \(ABC\) is congruent to triangle \(QPR\). The transformation here would be a combination of rotation (to align the angles) and reflection (to match the orientation) or just a rigid transformation (since congruent triangles can be mapped onto each other via rigid transformations: translations, rotations, reflections).

Answer:

1. The first drop - down (Triangle ABC is \(\boldsymbol{\text{congruent to}}\)) triangle QPR.
2. The second drop - down (the transformations are \(\boldsymbol{\text{rigid transformations (rotation/reflection)}}\)) (the exact wording may vary based on the drop - down options, but the key idea is that congruent triangles are related by rigid transformations).