Answers MISD-Geometry-RECOVERY-A-2019-2020Triangle Congruence: SSS and HL

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Given: HF || JK; HG ≅ JGProve: FHG ≅ KJG

FGH ≅ KGJ because vertical angles are congruent.

JKG ≅ HFG because vertical angles are congruent.

FHG ≅ JKG because right angles are congruent.

HFG ≅ KJG because alternate interior angles are congruent.

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Triangles D E F and D prime E prime F prime are connected at point E. Triangle D E F is rotated about point E to form triangle D prime E prime F prime.

dilation

reflection

rotation

translation

Triangles A B C and N M Q are shown. Sides B C and N M are congruent. Angles A B C and Q N M are congruent. Angles B C A and N M Q are both right angles.

A ≅ Q because of the third angle theorem.

AB ≅ QN because they are both opposite a right angle.

BC ≅ NM because it is given.

C ≅ M because right angles are congruent.

Which pair of triangles can be proven congruent by SAS?

2 triangles with identical angle measures are shown. The second triangle is shifted to the right.

2 triangles are shown. They have 2 congruent sides and a congruent angle. The first triangle is rotated about a point to form the second triangle.

2 triangles are shown. They have 1 congruent side and 2 congruent angles. The first triangle is rotated about a shared side to form the second triangle.

Option

The proof that ΔRST ≅ ΔVST is shown.Given: ST is the perpendicular bisector of RV.Prove: ΔRST ≅ ΔVST

perpendicular bisector theorem

converse of the perpendicular bisector theorem

Pythagorean theorem

SSS congruence theorem

How can ΔABC be mapped to ΔXYZ?

vertex B to vertex Z

vertex B to vertex Y

vertex A to vertex Z

vertex A to vertex Y

Triangles A B C and E D C are shown. Triangle A B C is rotated about point C to form triangle E D C.

a rotation about point B

a reflection across the line containing CB

a reflection across the line containing AC

a rotation about point C

Triangles W X Z and Y Z X share common side X Z. Angles W X Z and X Z Y are right angles. The lengths of sides W X and Z Y are 21 centimeters.

Yes, they are congruent by SAS.

Yes, they are both right triangles.

No, the triangles share side XZ.

No, there is only one set of congruent sides.

Triangles A B C and A B F are congruent. Triangle A B C is reflected across line B A to form triangle A B F.

a rotation about point A

a reflection across the line containing CB

a reflection across the line containing BA

a rotation about point B

Triangles A B C and D E F are shown. Triangle A B C is rotated to the left about point A and then is shifted up and to the right to form triangle D E F.

Translate vertex A to vertex D, and then reflect △ABC across the line containing AC.

Translate vertex B to vertex D, and then rotate △ABC around point B to align the sides and angles.

Translate vertex B to vertex D, and then reflect △ABC across the line containing AC.

Translate vertex A to vertex D, and then rotate △ABC around point A to align the sides and angles.

Triangles A B C and A D C share common side A C. The lengths of A B and A D are congruent.

Yes, but only if AB ≅ DC.

Yes, but only if BC ≅ DC.

No, because AB is not congruent to AC.

No, because AB ≅ DA.

Which pair of triangles can be proven congruent by the HL theorem?

2 right triangles have congruent hypotenuses.

2 triangles have one congruent angle and 2 congruent sides.

2 right triangles have congruent hypotenuses and another congruent side.

2 triangles have 3 congruent sides.

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