Question

for triangle dac and triangle zwx, angle d is congruent to angle z, angle a is congruent to angle w, and angle c is congruent to angle x. which statement must be true
a triangle dac is similar to triangle zwx.
b triangle dac and triangle zwx are right triangles.
c triangle dac has the same area as triangle zwx.
d triangle dac has the same perimeter as triangle zwx.

Explanation:

Step1: Recall the definition of similar triangles

Similar triangles have all corresponding angles congruent.

Step2: Analyze the given information

Since angle \(D\cong\angle Z\), angle \(A\cong\angle W\), and angle \(C\cong\angle X\), by the definition of similar triangles, triangle \(DAC\) and triangle \(ZWX\) have all corresponding angles congruent.

Step3: Evaluate other options

• Option B: There is no information given to suggest that these are right - triangles.
• Option C: Congruent angles do not imply equal area. Area also depends on side lengths.
• Option D: Congruent angles do not imply equal perimeter. Perimeter also depends on side lengths.

Answer:

A. Triangle \(DAC\) is similar to triangle \(ZWX\).