Question

1.) triangles qrs and xyz are congruent. answer the following questions:
a.) write the relationship between the sides for these two triangles.
b.) write the relationships between the angles of these two triangles.
c.) if side qs is equal to 16 and xz is equal to 3x - 20, find x.

Explanation:

Step1: Congruent triangles side - relationship

Since \(\triangle QRS\cong\triangle XYZ\), corresponding sides are equal. So \(QR = XY\), \(RS=YZ\), \(QS = XZ\).

Step2: Congruent triangles angle - relationship

Corresponding angles are equal. So \(\angle Q=\angle X\), \(\angle R=\angle Y\), \(\angle S=\angle Z\).

Step3: Solve for \(x\)

Given \(QS = 16\) and \(XZ=3x - 20\), and \(QS = XZ\) (from congruent triangles). Then \(3x-20 = 16\).
Add \(20\) to both sides: \(3x=16 + 20\), so \(3x=36\).
Divide both sides by \(3\): \(x=\frac{36}{3}\).

Answer:

a. \(QR = XY\), \(RS = YZ\), \(QS=XZ\)
b. \(\angle Q=\angle X\), \(\angle R=\angle Y\), \(\angle S=\angle Z\)
c. \(x = 12\)