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High School Core Standards - Geometry Assessment Anchors

5.03 Proving triangles congruent

Interactive practice questions

In the diagram, $MQ$MQ is perpendicular to $PR$PR, and $\Delta MPR$ΔMPR is isosceles.

a

What is the measure of $\angle MQR$MQR?

b

From the information given, we know $\triangle MPQ$MPQ and $\triangle MRQ$MRQ are congruent because:

they have three pairs of congruent sides.

A

they have two pairs of congruent sides and the non-included angle is congruent.

B

they have two pairs of congruent sides and the included angle is congruent.

C

they have three pairs of congruent angles.

D

they are both right triangles with hypotenuse and one leg the same length.

E

they have three pairs of congruent sides.

A

they have two pairs of congruent sides and the non-included angle is congruent.

B

they have two pairs of congruent sides and the included angle is congruent.

C

they have three pairs of congruent angles.

D

they are both right triangles with hypotenuse and one leg the same length.

E
c

Which congruence test matches our argument from the previous part?

Side-angle-side congruence (SAS)

A

Side-side-side congruence (SSS)

B

Angle-side-angle congruence (ASA)

C

Angle-angle-side congruence (AAS)

D

Hypotenuse-leg congruence (HL)

E

Side-angle-side congruence (SAS)

A

Side-side-side congruence (SSS)

B

Angle-side-angle congruence (ASA)

C

Angle-angle-side congruence (AAS)

D

Hypotenuse-leg congruence (HL)

E
Easy
Approx a minute
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This two-column proof shows that $\Delta ABC\cong\Delta XYZ$ΔABCΔXYZ in the attached diagram, but it is incomplete.

This two-column proof shows that $\Delta ABC\cong\Delta XYZ$ΔABCΔXYZ , but it is incomplete.

This two-column proof shows that $\Delta PQR\cong\Delta RSP$ΔPQRΔRSP in the attached diagram, but it is incomplete.

Outcomes

G.1.3.2.1

Write, analyze, complete, or identify formal proofs (e.g., direct and/or indirect proofs/proofs by contradiction).

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