Question

1. complete the creation as directed.
2. reflect on your creation.

similar triangles analysis
three triangular shapes were measured by different students. analyze the following triangular measurements to determine similarity relationships.
short response questions (6 questions)
question 2
are triangle abc and triangle xyz similar? justify your answer.

Explanation:

Step1: Calculate the third angle of each triangle

For triangle \(ABC\), using the angle - sum property of a triangle (\(\angle A+\angle B+\angle C = 180^{\circ}\)). Given \(\angle A = 50^{\circ}\), \(\angle B=60^{\circ}\), then \(\angle C=180^{\circ}-(50^{\circ}+60^{\circ}) = 70^{\circ}\).
For triangle \(XYZ\), given \(\angle X = 50^{\circ}\), \(\angle Y = 70^{\circ}\), then \(\angle Z=180^{\circ}-(50^{\circ}+70^{\circ})=60^{\circ}\).

Step2: Check the AA (Angle - Angle) similarity criterion

The AA similarity criterion states that if two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar.
In \(\triangle ABC\) and \(\triangle XYZ\), \(\angle A=\angle X = 50^{\circ}\), \(\angle B=\angle Z = 60^{\circ}\), \(\angle C=\angle Y = 70^{\circ}\).

Answer:

Yes, Triangle \(ABC\) and Triangle \(XYZ\) are similar. By the AA (Angle - Angle) similarity criterion, since \(\angle A=\angle X\), \(\angle B=\angle Z\), and \(\angle C=\angle Y\), the two triangles have all three pairs of corresponding angles equal, so \(\triangle ABC\sim\triangle XYZ\).