Topics
6. Congruence & Triangles
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United States of AmericaVirginia
Geometry

6.03 SSS and SAS congruence criteria

Lesson
Practice
Adaptive
Worksheet

Interactive practice questions

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

Statements Reasons
$\overline{CB}\cong\overline{ZY}$CB≅ZY Given
$\overline{AC}\cong\overline{XZ}$AC≅XZ

Given

$\overline{AB}\cong\overline{XY}$AB≅XY

 Given

$\Delta ABC\cong\Delta XYZ$ΔABC≅ΔXYZ

 $\left[\text{____}\right]$[____]

Select the correct reason to complete the proof.

Side-angle-side congruence (SAS)

A

Angle-angle-side congruence (AAS)

B

Side-side-angle congruence (SSA)

C

Side-side-side congruence (SSS)

D

Angle-side-angle congruence (ASA)

E
Medium
< 1min

Consider the adjacent figure:

Medium
< 1min

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

Medium
< 1min

This two-column proof shows that $\Delta DEH\cong\Delta FEG$ΔDEH≅ΔFEG in the attached diagram, but it is incomplete.

Medium
< 1min
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Outcomes

G.TR.2

The student will, given information in the form of a figure or statement, prove and justify two triangles are congruent using direct and indirect proofs, and solve problems involving measured attributes of congruent triangles.

G.TR.2a

Use definitions, postulates, and theorems (including Side-Side-Side (SSS); Side-Angle-Side (SAS); Angle-Side-Angle (ASA); Angle-Angle-Side (AAS); and Hypotenuse-Leg (HL)) to prove and justify two triangles are congruent.

G.TR.2b

Use algebraic methods to prove that two triangles are congruent.

G.TR.2d

Given a triangle, use congruent segment, congruent angle, and/or perpendicular line constructions to create a congruent triangle (SSS, SAS, ASA, AAS, and HL).

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