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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

2. Congruent Triangles

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Exercise 1 Page 347

When two angles have the same number of markers, this indicates that the angles are congruent. Similarly, when two sides have the same number of markers, the sides are congruent.

Corresponding Angles: ∠ Y ≅ ∠ S, ∠ X ≅ ∠ R, ∠ XZY ≅ ∠ RZS
Corresponding Sides: YX ≅ SR, YZ ≅ SZ, XZ ≅ RZ
Congruence Relation: △ XYZ≅△ SRZ

Practice makes perfect

If all of the corresponding parts are congruent, then the two polygons are congruent. Therefore, to show that the two triangles are congruent, we should check for congruent angles and congruent sides.

Checking Angles

Let's first focus on the angles of the given triangles.

The markers on the angles tell us about the congruence relationships between the angles of the triangles. If two angles have the same number of markers, then they are congruent.

∠ Y &≅ ∠ S ∠ X &≅ ∠ R ∠ XZY &≅ ∠ RZS All angles in △ XYZ have congruent pairs in △ RSZ.

Checking Sides

Now let's check the sides.

The markers on the sides tell us about the congruence relationships between the sides of the triangles. In other words, if two sides have the same number of markers it means they are congruent. YX &≅ SR YZ &≅ SZ XZ &≅ RZ All sides of △ XYZ have congruent pairs in △ SRZ.

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. △ XYZ ≅△ SRZ

Subchapter links

Exercises p.347-352