Question

1. two triangle - shaped lots are congruent. find the missing side lengths and angle measures.
2. in the figures, ( \triangle cdacong\triangle xyz ). name the congruent angles.

Explanation:

Step1: Analyze congruent triangles properties

Congruent triangles have corresponding sides and angles equal.

Step2: Match sides and angles

In the first pair of congruent right - angled triangles:

• The side of length \(140\) ft in the first triangle corresponds to \(x\) in the second triangle (\(x = 140\) ft).
• The side of length \(186.7\) ft in the first triangle corresponds to \(v\) in the second triangle (\(v=186.7\) ft).
• The angle of \(38^{\circ}\) in the first triangle corresponds to \(y\) in the second triangle (\(y = 38^{\circ}\)).
• The angle of \(52^{\circ}\) in the second triangle corresponds to \(w\) in the first triangle (\(w = 52^{\circ}\)).
• The right - angle (\(90^{\circ}\)) is common property ( \(z = 90^{\circ}\)).

For \(\triangle CDA\cong\triangle XYZ\), by the property of congruent triangles (corresponding parts of congruent triangles are equal), \(\angle C\cong\angle X\), \(\angle D\cong\angle Y\), \(\angle A\cong\angle Z\)

Answer:

For the first problem: D. \(v = 186.7\) ft; \(w = 52^{\circ}\); \(x=140\) ft; \(y = 38^{\circ}\); \(z = 90^{\circ}\)
For the second problem: B. \(\angle C\cong\angle X,\angle D\cong\angle Y,\angle A\cong\angle Z\)