Question

Question 2 Keep the triangle that you created in Question 1. You will now copy the triangle to a different location on the grid using two of its angles and the included side: In a different place on the grid, draw a new line segment of the same length as the line segment recorded in Question 1. (This will be easier if you draw the new line segment parallel or perpendicular to the corresponding line segment from Question 1.) At each endpoint of the new line segment, create an angle of a given size. Size the angles using the angle measurements you recorded in Question 1. Once you’ve created the angles, draw a ray through each endpoint at the specified angle measurement.

What do you notice about the two triangles in terms of their size and shape?

Options:
A) The two triangles are congruent in size and shape.
B) The two triangles are similar in size and shape.
C) The two triangles are different in size but similar in shape.
D) The two triangles are different in both size and shape.

Answer 1

When constructing a new triangle using two angles and the included side from an original triangle, the two triangles are congruent in size and shape by the Angle-Side-Angle (ASA) Postulate.

Step-by-step explanation:

When you create a new triangle on the grid by drawing a line segment equal in length to the one from the original triangle and then constructing angles at each endpoint with the same measurements as those recorded from the original triangle, what you end up with are two triangles of the same size and shape. This is because when two triangles have two angles and the included side between them that are congruent, they are considered to be congruent by the Angle-Side-Angle (ASA) Postulate. Therefore, the correct answer to the question is:

A) The two triangles are congruent in size and shape.

By constructing the triangles this way, you are effectively repeating the same measurements and angle sizes, which ensures that both triangles will be identical. This property of congruence is a fundamental aspect of triangle geometry.