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―

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falhiblesw · Accepted Answer

a. HB― and HE― are side lengths of △HBC and △HDE. Therefore, to prove HB―≅HE―, we must prove △HBC≅△HDE. b. Proof Outline: Since the pentagon is equilateral, then we know ED―≅BC―. Vertical angles are congruent so we also know ∠EHD≅∠CHB. This is not enough to prove the triangles are congruent though. Since the pentagon is equiangular, we know ∠BCD≅∠EDC. We can then prove that △BCD≅△EDC by SAS. Using CPCTC, we then have ∠HBC≅∠HED. We now have two pairs of congruent corresponding angles and a pair of congruent nonincluded sides so then △HBC≅△HDE by AAS. Proof: Statements Reasons 1.ABCDE is an equilateral and 1. Given equiangular pentagon 2.ED≅BC 2. Def. of equilateral 3.∠EHD≅∠CHB 3. Vertical Angles Theorem 4.&amp;lt;BCD≅&amp;lt;EDC 4. Def. of equiangular 5.CD≅CD 5. Reflexive Property 6.△BCD≅EDC 6. SAS 7.&amp;lt;HBC≅&amp;lt;HED 7. CPCTC 8.△HBC≅△HDE 8.AAS

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¯.

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