NY-G.CO.8

GeometryCongruence60 target questions

Explain how the criteria for triangle congruence (ASA SAS SSS AAS and HL) follow from the definition of congruence in terms of rigid motions.

Sample Practice Questions (3)

Given

△ A B C

and

△ D E F

, if

\overline{A B} ≅ \overline{D E}

∠ B ≅ ∠ E

, and

\overline{B C} ≅ \overline{E F}

, which rigid motion sequence could be used to prove the triangles are congruent by the SAS criterion?

AA translation mapping

B

E

, followed by a rotation about

E

mapping

B A

E D

, and a reflection if necessary.

BA dilation with a scale factor of

k = 1

centered at the origin.

CA translation mapping

A

F

and a rotation mapping

C

D

DA reflection across the perpendicular bisector of

\overline{A C}

To use the Hypotenuse-Leg (HL) theorem to prove two triangles are congruent, which of the following conditions must be met?

AThe triangles must be acute.

BThe triangles must be right triangles.

CAll three sides must be congruent.

DTwo angles and the included side must be congruent.

In right triangles

△ J K L

and

△ M N O

∠ K

and

∠ N

are right angles. If

\overline{J L} ≅ \overline{M O}

and

\overline{K L} ≅ \overline{N O}

, are the triangles congruent? If so, by what criterion?

AYes, by SAS

BYes, by SSS

CYes, by HL

DNo, the triangles are not necessarily congruent.

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