The pentagon at the right is equilateral and equiangular.a. What two triangles must be congruent to prove HB¯≅HE¯?b. Write a proof to show HB¯≅HE¯.

zi2lalZ 2020-11-22 Answered

The pentagon at the right is equilateral and equiangular.
a. What two triangles must be congruent to prove HBHE?
b. Write a proof to show HBHE

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Expert Answer

falhiblesw
Answered 2020-11-23 Author has 97 answers

a. HB and HE are side lengths of HBC and HDE. Therefore, to prove HBHE, we must prove HBCHDE.
b. Proof Outline: Since the pentagon is equilateral, then we know EDBC. Vertical angles are congruent so we also know EHDCHB. This is not enough to prove the triangles are congruent though. Since the pentagon is equiangular, we know BCDEDC. We can then prove that BCDEDC by SAS. Using CPCTC, we then have HBCHED. We now have two pairs of congruent corresponding angles and a pair of congruent nonincluded sides so then HBCHDE by AAS.
Proof:
Statements Reasons
1.ABCDE is an equilateral and 1. Given equiangular pentagon
2.EDBC 2. Def. of equilateral
3.EHDCHB 3. Vertical Angles Theorem
4.<BCD<EDC 4. Def. of equiangular
5.CDCD 5. Reflexive Property
6.BCDEDC 6. SAS
7.<HBC<HED 7. CPCTC
8.HBCHDE 8.AAS

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