Chapter 4.3, Problem 9CYU

To determine

Toshow: that the polygons are congruent by identifying all congruent corresponding parts.

Answer to Problem 9CYU

  $\Delta XYZ\cong \Delta ABC$ .

Explanation of Solution

Given:

Concept used:

Condition of congruence triangle:

Side angle side $\left(SAS\right)$ : two side and one angle of one triangle is equivalent another triangle.

Side-side-side $\left(SSS\right)$ : all three side of the one triangle is equivalent to another triangle.

Angle side angle $\left(ASA\right)$ : two angle and side included between the angles of one triangle is equivalent to another two angle and side included between the angles of triangle.

Angle-angle side $\left(AAS\right)$ :

two angle and non-included side between the angles of one triangle is equivalent to another two angle and non-included side between the angles of triangle.

Right angle hypotenuse side $\left(RHS\right)$ : Hypotenuse and side of a right-angled triangle is equivalent to the hypotenuse and side of the second right angled triangle.

Calculation:

Angle:

  $\angle X\cong \angle Y$ , because right angles are congruent.

$\angle Z\cong \angle C$ , because there has the same measure $30$ .

$\angle Y\cong \angle B$ , because there has the same measure $60$ .

Sides:

$\overline{XY}\cong \overline{AB}$ , because there has the same length $2.5$ .

$\overline{XZ}\cong \overline{AC}$ , because there has the same length $4.3$ .

$\overline{YZ}\cong \overline{BC}$ , because, there has the same length $5$ .

All corresponding parts of the two triangles are congruent.

Hence, $\Delta XYZ\cong \Delta ABC$ .