SophiaSuhelidn
Answered

IDNLearn.com provides a collaborative platform for sharing and gaining knowledge. Find reliable solutions to your questions quickly and accurately with help from our dedicated community of experts.

ΔABC is an equilateral triangle with AD perpendicular to BC. Prove that ΔADB ≅ ΔADC.

Sagot :

Cinderofsoulsssidn

Step-by-step explanation:

An equilateral triangle means all sides are congruent.

AB≅BC≅AC

All angles are also congruent.

∠ABC≅∠BCA≅∠CAB

AD being perpendicular makes it a bisector of both BC and ∠CAB.

BD≅CD

∠BAD≅∠CAD

Now, there are multiple ways to prove that ΔADB≅ΔADC. All 3 sides and all 3 angles of both triangles are congruent, so you could do it however you want.

1) ASA (one of the possible ASA combinations)

  • ∠ABD ≅ ∠ACD because this is an equilateral triangle
  • BD ≅ CD because AD bisects BC
  • ∠BDA ≅ ∠CDA because AD is perpendicular to BC, both 90°

2) HL (again, one of the multiple possible HL combinations)

  • AD is perpendicular to BC, creating 2 right triangles
  • AB ≅ AC because ΔABC is equilateral
  • AD ≅ DA by the reflexive property, it is congruent to itself

There are many more but I won't write them all out.

View image Cinderofsoulsss
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Discover insightful answers at IDNLearn.com. We appreciate your visit and look forward to assisting you again.