a Examining the diagram, we notice that the triangles have a pair of congruent sides and a pair of congruent angles. Additionally, the two triangles share a side. According to the 'Reflexive Property of Congruence this side must be congruent as well. Let's add this to the diagram and label the vertices.
To find the value of x, we recognize that AB and CD are corresponding congruent sides. Since we have been given expressions containing x for both of these sides, we can equate them and solve for x.
From the diagram we see that the triangles are right triangles. If we can prove that a pair of legs and the hypotenuses are congruent, we can use the HL (Hypotenuse-Leg) Congruence Theorem to prove congruence. By using the Pythagorean Theorem we can calculate the unknown leg or hypotenuse in either of the triangles.
As we can see, the two triangles have congruent hypotenuses and a pair of congruent legs. Therefore, they are congruent according to the HL Congruence Theorem. Let's show this as a flowchart.
Examining the diagram we see that x spans part of the hypotenuse in one of the triangles. Since the second part of the hypotenuse coincide with the shorter leg of the other triangle, which must be 9, we can write and solve an equation for x.
x+9=41 ⇔ x=32
