EDC is an isosceles triangle.
According to which theorem are the triangles congruent?
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EDC is an isosceles triangle.
According to which theorem are the triangles congruent?
ΔEDC is an isosceles triangle.
DE = EC
(A)
(A)
Reasoning:
In an isosceles triangle there are 2 equal sides.
The base angles of an isosceles triangle are equal.
Therefore, the triangles are congruent according to the theorem S.A.S. theorem.
A.S.A.
Look at the triangles in the diagram.
Which of the statements is true?
Look at what's given and what you can deduce. Here you have: equal angles ∢ADE = ∢BCE, vertical angles at E are equal, and the sides DE = EC from the isosceles triangle. That's A-S-A!
For S.A.S., you need two sides and the included angle between them. Here, the angle at E is between the equal sides DE and EC, but we're proving different triangles (ADE and BCE). The pattern is angle-side-angle.
An isosceles triangle has two equal sides and two equal base angles. Since EDC is isosceles with vertex E, we know DE = EC and the base angles ∠EDC = ∠ECD are equal.
Vertical angles are opposite angles formed when two lines intersect. At point E, lines AEB and DEC intersect, creating vertical angles. So ∠AED and ∠BEC are equal (vertical angles).
No, because we're not given information about all three sides of each triangle. We only know DE = EC from the isosceles property and AC = BD, but that's not enough for S.S.S.
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