Consider the Hinge Theorem. Remember that since two sides have the same length, they are congruent.
x>4
Practice makes perfect
We will start by looking closer at the given triangles. Note that if two sides have the same length, they are congruent. Also, according to the Reflexive Property of Congruence, every side is congruent to itself. Let's mark it on the diagram.
For the given triangles, we will find the range of possible values for x. In order to do that, we will use the following theorem.
If two sides of one triangle are congruent to two sides of another triangle, and the included angles are not congruent, then the longer third side is opposite the larger included angle.
Applying the theorem, we can order the sides of the given triangles.
135^(∘) &> 95^(∘)
&⇓
3x-2 &> 10
Let's solve the inequality for x.
