When the bisectors of two consecutive angles of a
parallelogram meet at a point on the remaining side,
what type of triangle is:
a) âˆ†DEC? | b) âˆ†ADE? | c) âˆ†BCE? |
a.
To find:
The type of the angle in ∆DECwhen the bisectors of two consecutive angles of the parallelogram ABCD meet at a point on the remaining side.
Given:
The bisectors of two consecutive angles of the parallelogram ABCD are shown below.
Corollary:
A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.
In the given parallelogram ABCD.
PROOF | |
Statements | Reasons |
1. Parallelogram ABCD | 1. Given |
2. |
2. By the definition of a parallelogram |
3. |
3. Since DE and CE are angle bisectors of |
4 |
b.
To find:
The type of the angle in ∆ADEwhen the bisectors of two consecutive angles of the parallelogram ABCD meet at a point on the remaining side.
c.
To find:
The type of the angle in ∆BCEwhen the bisectors of two consecutive angles of the parallelogram ABCD meet at a point on the remaining side.
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