Question

Use the information below to solve for x, y, and z.

Hint draw and fully lable the triangles.
Answer
X=
Z=
AABC=ADEF;
AB= 4cm, BC = x,
AC = 5cm; DE = (2y - 5);
EF = 3; and DF = (3z + 2).

Answer 1

To solve x, y, and z, we need to use the fact that AABC and ADEF are congruent triangles. This means that their corresponding sides and angles are equal. We can use the following notation to indicate the correspondence: AABC ≅ ADEF.

We can write three equations based on the congruence of the corresponding sides:

AB = DE BC = EF AC = DF

Substituting the given values, we get:

4 = 2y - 5 x = 3 5 = 3z + 2

Solving for y, we get:

4 + 5 = 2y 9 = 2y y = 9/2

Solving for z, we get:

5 - 2 = 3z 3 = 3z z = 1

Therefore, the values of x, y, and z are:

x = 3

y = 9/2

z = 1