IXL - Proofs involving triangles and quadrilaterals (Geometry practice)

∥

and

≅

Complete the proof that

≅

	Statement	Reason
1	segmentsegmentQR is parallel to segmentsegmentST	Given
2	segmentsegmentST is congruent to segmentsegmentQR	Given
3	∠QST is congruent to ∠RQS	Alternate Interior Angles Theorem
4	segmentsegmentQS is congruent to segmentsegmentQS	Reflexive Property of Congruence
5	△QRS is congruent to △STQ
6	segmentsegmentQT is congruent to segmentsegmentRS

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Learn with an example

question

≅

and

∥

Complete the proof that

≅

	Statement	Reason
1	segmentsegmentHI is congruent to segmentsegmentFG	Given
2	segmentsegmentFG is parallel to segmentsegmentHI	Given
3	∠FHI is congruent to ∠GFH	Alternate Interior Angles Theorem
4	segmentsegmentFH is congruent to segmentsegmentFH	Reflexive Property of Congruence
5	△FGH is congruent to △HIF	Text field with dropdown. Use the down arrow key to hear the options, press spacebar to select.
6	segmentsegmentFI is congruent to segmentsegmentGH	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 5 and 6.

Line 5:

SAS lets you deduce

△

≅

△

from

≅

in line 1,

∠

FHI

≅

∠

GFH

in line 3, and

≅

in line 4.

Line 6:

CPCTC lets you deduce

≅

from

△

≅

△

in line 5.

	Statement	Reason
1	segmentsegmentHI is congruent to segmentsegmentFG	Given
2	segmentsegmentFG is parallel to segmentsegmentHI	Given
3	∠FHI is congruent to ∠GFH	Alternate Interior Angles Theorem
4	segmentsegmentFH is congruent to segmentsegmentFH	Reflexive Property of Congruence
5	△FGH is congruent to △HIF	SAS
6	segmentsegmentFI is congruent to segmentsegmentGH	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:

O.12Properties of quadrilaterals: mixed practice

L.9Proofs involving corresponding parts of congruent triangles

Lesson: Proofs with congruent triangles

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