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3 years ago

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Mathematics

2 answers:

vivado [14]3 years ago

7 0

Answer:

Option D is correct

CPCT

Step-by-step explanation:

Given: In an isosceles triangle ΔHKJ with $KH \cong KJ$

Construct KM, a bisector of the base HJ.

to prove: $\angle H \cong \angle J$

In ΔKHM and ΔKJM

$\overline{KM}$ bisects $\overline{HJ}$ [Given]

Segment bisectors states that a line or segment which cuts another line segment into two equal parts.

then, by definition of Segment bisector :

$\overline{HM} \cong \overline{JM}$

$KH \cong KJ$ [Given]

Reflexive property of congruence that any geometric figure is congruent to itself.

$\overline{KM} \cong \overline{KM}$ [by definition of Reflexive property of congruence]

SSS(Side-Side-Side) Postulates states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

therefore, by SSS postulates

ΔKHM $\cong$ ΔKJM

By CPCT [Corresponding Part of congruent Triangle]

$\angle H \cong \angle J$ proved!

Lena [83]3 years ago

4 0

The answer is D, because in the step before that it was proved that the triangles were congruent and CPCTC is used after they are proved congruent.

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