Exercise 10 Page 348

To show that the two triangles are congruent, we can check for congruent angles and congruent sides.

Checking Angles

Let's first check the angles. Notice that because GHKJ is a rectangle, ∠ JGK and ∠ HKG are alternate interior angles as well as ∠ GKJ and ∠ KGH. By the Alternate Interior Angles Theorem, we can conclude that these angles are congruent.

From here, we can determine the congruence relationships between the angles of the triangles. ∠ KJG &≅ ∠ GHK ∠ JGK &≅ ∠ HKG ∠ GKJ &≅ ∠ KGH All angles of △ JGK have congruent pairs in △ HKG.

Checking Sides

Now let's check the sides. We can see that GK is a common side for both triangles.

Therefore, the congruence relationships between the sides of the triangles can be written as follows. GK &≅ GK KJ &≅ GH JG &≅ HK All sides of △ JGK have congruent pairs in △ HKG.

Conclusion

Since the vertices of the two triangles can be paired up so that the corresponding angles and sides are congruent, the two triangles are congruent. △ J G K ≅ △ H K G