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McGraw Hill Glencoe Geometry, 2012

MH

McGraw Hill Glencoe Geometry, 2012 View details

3. Congruent Triangles

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Exercise 2 Page 258

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: $∠ A ≅ ∠ E,$ $∠ B ≅ ∠ F,$ $∠ C ≅ ∠ G,$ $∠ D ≅ ∠ H,$
Corresponding Sides: $\overline{A B} ≅ \overline{E F},$ $\overline{B C} ≅ \overline{F G},$ $\overline{C D} ≅ \overline{G H},$ $\overline{D A} ≅ \overline{H E}$
Congruence Relation: $A B C D ≅ E F G H$

Practice makes perfect

To show that the polygons are congruent, we have to check for congruent angles and congruent sides.

Checking Angles

Let's first check the angles.

The markers on the angles tell us about the congruence relationships between the angles.

∠ A ∠ B ∠ C ∠ D ≅ ∠ E ≅ ∠ F ≅ ∠ G ≅ ∠ H

All angles in

A B C D

have congruent pairs in

E F G H .

Checking Sides

Now let's check the sides.

The markers on the sides tell us about the congruence relationships between the sides.

\overline{A B} \overline{B C} \overline{C D} \overline{D A} ≅ \overline{E F} ≅ \overline{F G} ≅ \overline{G H} ≅ \overline{H E}

All sides of

A B C D

have congruent pairs in

E F G H .

Conclusion

Since the vertices of the two polygons can be paired up so that the corresponding angles and sides are congruent, the two polygons are congruent.

A B C D ≅ E F G H

Subchapter links

Check Your Understanding p.258-259

Practice and Problem Solving p.259-262

H.O.T. Problems p.262

Standardized Test Practice p.263

Spiral Review p.263

Skills Review p.263