McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
1. Angles of Polygons
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Exercise 64 Page 483

Look at the markers on the sides and at the angles.

∠ RSV ≅ ∠ TSV, ∠ R ≅ ∠ T, ∠ SVR ≅ ∠ SVT
RV ≅ TV, SV ≅ SV, SR ≅ ST
△ SVR≅△ SVT

Practice makes perfect

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.

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

∠ RSV &≅ ∠ TSV ∠ R &≅ ∠ T ∠ SVR &≅ ∠ SVT All angles in triangle △ SVR have congruent pairs in triangle △ SVT.

Checking Sides

Now let's check the sides. Notice that SV is a shared side between both triangles which means its congruent according to the Reflexive Property of Congruence.

The markers on the sides tell us about the congruence relationships between the sides of the triangles. RV &≅ TV SV &≅ SV SR &≅ ST All sides of triangle △ SVR have congruent pairs in triangle △ SVT.

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. △ SVR ≅△ SVT