Virginia SOL Math / Geometry / Triangles

G.TR.2

Triangle Congruence

What you'll learn

  • Identify congruent triangles using SSS, SAS, ASA, AAS, and HL
  • Write congruence statements with corresponding parts
  • Use congruence to find unknown side lengths and angles

Words to know

Congruent —
same size and same shape
Corresponding parts —
matching sides or angles of two figures
SSS —
three pairs of equal sides prove congruence
SAS —
two sides and the included angle prove congruence
ASA —
two angles and the included side prove congruence

Why it matters Proving triangles congruent guarantees that manufactured parts, roof trusses, and folded designs match exactly every time.

Worked examples

Model ItI do

Triangle ABC and triangle DEF have the marked parts equal. Which rule proves them congruent, and what is the congruence statement?

The tick marks show one pair of equal sides, and the shapes are built with two more matching sides, so all three sides match: SSS. The congruence statement is triangle ABC is congruent to triangle DEF.

Try It TogetherWe do

In triangles PQR and STU, PQ = ST, angle Q = angle T, and QR = TU. Which rule applies?

Two sides and the angle between them match: side PQ, included angle Q, side QR. That is SAS, so triangle PQR is congruent to triangle STU.

Now YouYou do

Two triangles have two pairs of equal angles and a pair of equal non-included sides. Which congruence rule proves them congruent?

Match the given parts to a rule (think AAS). Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Which rule proves two triangles congruent using three pairs of equal sides?

  2. 2.In congruent triangles, corresponding angles are _____.

  3. 3.If triangle ABC is congruent to triangle XYZ and AB = 9, what is XY?

On Level

The core Quick Check from the book.

  1. 1.Which rule uses three pairs of equal sides?

  2. 2.If two right triangles have equal hypotenuses and one equal leg, which rule applies?

  3. 3.In congruent triangles, corresponding angles are _____.

  4. 4.SAS stands for side, _____, side.

  5. 5.If triangle ABC is congruent to triangle XYZ and AB = 7, what is XY?

Challenge

Stretch your thinking.

  1. 1.Two right triangles have equal hypotenuses and one pair of equal legs. Which rule proves them congruent?

  2. 2.Two triangles have two pairs of equal angles and a pair of equal NON-included sides. Which rule proves them congruent?

  3. 3.In triangles PQR and STU, angle P = angle S, PQ = ST, and angle Q = angle T. Which rule applies?