Download Isosceles and Equilateral Triangles

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LESSON
7-2
Isosceles and Equilateral Triangles
Reading Strategies: Comparison Chart
Isosceles and equilateral triangles can be described in the following ways.
Theorem or Corollary
Hypothesis and
Conclusion
Isosceles Triangle Theorem
If two sides of a triangle are congruent,
then the angles opposite those sides are
congruent.
If XZ ≅ XY ,
then ∠Y ≅ ∠Z.
Converse of Isosceles Triangle
Theorem
If two angles of a triangle are congruent,
then the sides opposite those angles are
congruent.
If ∠N ≅ ∠M,
then LM ≅ LN .
Equilateral Triangle Corollary
If a triangle is equilateral,
then it is equiangular.
(equilateral
→ equiangular )
If QR ≅ RS ≅ SQ ,
then ∠Q ≅ ∠R ≅ ∠S.
Equiangular Triangle Corollary
If a triangle is equiangular,
then it is equilateral.
(equiangular
→ equilateral )
If ∠E ≅ ∠F ≅ ∠G,
then EF ≅ FG ≅ GE .
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Example
Use the chart to do Problems 1–3.
1. Read each theorem or corollary aloud slowly. At the same time, point
to the parts of the example triangle in the third column. For example, “If
two sides of a triangle are congruent” (point to XZ and XY ), “then the
angles opposite those sides are congruent” (point to ∠Y opposite XZ,
and ∠Z opposite XY ).
2. One angle of an isosceles triangle measures 40°. Draw and label two
different isosceles triangles that have a 40° angle.
3. Can a triangle have a 60° angle and exactly two congruent sides?
Explain your answer using the information about equilateral and
isosceles triangles.
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