## Congruent Triangle Proofs (Part 2)Method 2: ASA (Angle, Side, Angle) You can also prove that two triangles are congruent by showing that two angles and the included side are congruent. In this example, < R is congruent to < X, < S is congruent to < W and side RS is congruent to side XW. (Note that the side must be between the two angles.) Let's take a look at how to use this congruence in a proof. Given: < ABD ≅ < CBDProve: D is the midpoint of ACFirst let's determine what we know. We have been given a pair of congruent angles and a pair of congruent sides. We also know that the larger triangle around the outside is isosceles. How does that help us? Because the triangle is isosceles, we know that it has two congruent sides and two congruent angles. So we can say that < A is congruent to < C. Let's show this in the table:
Here we have shown that the two pieces on the bottom are equal in size. That means that point D is in the middle of them. And therefore, D must be the midpoint of the segment AC.
Let's Recap! We used given information along with definitions to show that two triangles were congruent using Angle, Side, Angle. Once the two triangles are shown to be congruent, we were able to also say that all other corresponding sides or corresponding angles are also congruent. If these additional congruent pieces do not complete the proof, be sure to use other known definitions.
To link to this |
## More Topics## Educational Videos |