In the diagram shown, AE 1/3AC and ED ll CB. Explain why df must be one-fourth length of CD
1 answer:
The value of the length DF is 1/4 of that of CD because of the Angle Bisector Theorem for triangles.
<h3>What is the Angle Bisector Theorem?</h3>
The Angel Bisector Theorem states that if a ray bisects an angle of a triangle, it dissects the side of the triangle that is opposite to the dissected angle into parts that are proportionate to the adjacent sides.
Note that the angle that has been dissected here is ∠CBD. Thus,
=
See the link below for more about Angle Bisector Theorem of the Triangle:
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<u>Question 11</u>
1) ,
(given)
2) (reflexive property)
3) (ASA)
4) (CPCTC)
<u>Question 12</u>
1) Isosceles with
,
(given)
2) (angles opposite congruent sides in a triangle are congruent)
3) and
are supplementary.
and
are supplementary (angles that form a linear pair are supplementary)
4) (supplements of congruent angles are congruent)
5) (SAS)
6) (CPCTC)
7) is an isosceles triangle (a triangle with two congruent sides is isosceles)
<em>Note: I changed the names of the segments in Question 11 because of the word filter.</em>