Question

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4.
Given: KH≅KJ,KM bisectsHJ .
Prove: ∠H ≅ ∠J

Supply the missing reason in Statement 6 of the proof of the Isosceles Triangle Theorem.

Begin with isosceles ∆HKJ with KH≅KJ . Construct KM , a bisector of the base HJ.

A)SSS Postulate
B)Definition of segment bisector
C)Reflexive Property of Congruence
D) CPCTC

Answer 1

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!

Answer 2

Answer:

CPCTC

Step-by-step explanation: