Answer:
- You can use HL congruence and CPCTC
Step-by-step explanation:
You want a proof that the right triangles shown in an isosceles trapezoid are congruent, and another triangle is isosceles.
HL
Your approach seems to get sidetracked at about step 5. You cannot do anything with angles 5–8 until after you prove ∆AEB is isosceles. It looks like more work than necessary.
You might try going at it this way:
2) ED ≅ EC . . . . . ∆EDC is isosceles (definition of isosceles triangle)
3) DA ≅ CB . . . . . definition of isosceles trapezoid
4) ∠ADE and ∠BCE are right angles . . . . . definition of perpendicular lines
5) ∆ADE ≅ ∆BCE . . . . . HL congruence postulate
6) AE ≅ BE . . . . . CPCTC
7) ∆AEB is isosceles . . . . . definition of isosceles triangle
SSA
There is no such thing as an SSA congruence (or similarity) theorem or postulate. The closest you get to that is the HL congruence postulate applicable only to right triangles.
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Additional comment
The problem with SSA is that there can be two solutions to the triangle if the angle is opposite the shorter side. When it is a right triangle, we call that postulate the HL congruence postulate.
CPCTC = Corresponding Parts of Congruent Triangles are Congruent
