IXL - Proofs involving isosceles triangles (Geometry practice)

Complete the proof that

≅

	Statement	Reason
1	∠J is congruent to ∠I	Given
2	segmentsegmentIJ is perpendicular to segmentsegmentHK	Given
3	∠HKI is congruent to ∠HKJ	All right angles are congruent
4	segmentsegmentHK is congruent to segmentsegmentHK	Reflexive Property of Congruence
5	△HIK is congruent to △HJK
6	segmentsegmentJK is congruent to segmentsegmentIK

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Learn with an example

question

is the midpoint of

and

⟂

Complete the proof that

≅

	Statement	Reason
1	K is the midpoint of segmentsegmentIJ	Given
2	segmentsegmentIJ is perpendicular to segmentsegmentHK	Given
3	∠HKI is congruent to ∠HKJ	All right angles are congruent
4	segmentsegmentIK is congruent to segmentsegmentJK	Definition of midpoint
5	segmentsegmentHK is congruent to segmentsegmentHK	Reflexive Property of Congruence
6	△HIK is congruent to △HJK	Text field with dropdown. Use the down arrow key to hear the options, press spacebar to select.
7	segmentsegmentHI is congruent to segmentsegmentHJ	Text field with dropdown. Use the down arrow key to hear the options, press spacebar to select.

solution

Choose the reasons that justify the statements on lines 6 and 7.

Line 6:

SAS lets you deduce

△

≅

△

from

∠

HKI

≅

∠

HKJ

in line 3,

≅

in line 4, and

≅

in line 5.

Line 7:

CPCTC lets you deduce

≅

from

△

≅

△

in line 6.

	Statement	Reason
1	K is the midpoint of segmentsegmentIJ	Given
2	segmentsegmentIJ is perpendicular to segmentsegmentHK	Given
3	∠HKI is congruent to ∠HKJ	All right angles are congruent
4	segmentsegmentIK is congruent to segmentsegmentJK	Definition of midpoint
5	segmentsegmentHK is congruent to segmentsegmentHK	Reflexive Property of Congruence
6	△HIK is congruent to △HJK	SAS
7	segmentsegmentHI is congruent to segmentsegmentHJ	CPCTC

Looking for more? Try these:

Lesson: Proofs with congruent triangles

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Work it out

Not feeling ready yet? These can help:

L.10Congruency in isosceles and equilateral triangles

L.8Proving triangles congruent by SSS, SAS, ASA, and AAS

Lesson: Proofs with congruent triangles

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