5. Triangles & Congruence

In the diagram, $MQ$`M``Q` is perpendicular to $PR$`P``R`, and $\Delta MPR$Δ`M``P``R` is isosceles.

a

What is the measure of $\angle MQR$∠`M``Q``R`?

b

From the information given, we know $\triangle MPQ$△`M``P``Q` and $\triangle MRQ$△`M``R``Q` 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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