Virginia SOL Math / Grade 6 / Measurement & Geometry

6.MG.4

Congruence

What you'll learn

  • Determine the congruence of line segments and angles
  • Determine the congruence of polygons
  • Identify congruent figures in context

Words to know

Congruent —
having exactly the same size and shape
Line segment —
a straight part of a line with two endpoints
Angle —
the figure formed by two rays from one point
Polygon —
a closed shape with straight sides
Corresponding —
matching parts in the same position

Why it matters Manufactured parts, floor tiles, and design patterns rely on identical pieces, so recognizing congruence checks that shapes truly match.

Worked examples

Model ItI do

Are two line segments that both measure 7 cm congruent?

Line segments are congruent when they have equal length. Since both measure 7 cm, they are congruent.

Try It TogetherWe do

Two angles measure 45 degrees and 50 degrees. Are they congruent?

Angles are congruent only when they have the same measure. Since 45 degrees does not equal 50 degrees, the angles are not congruent.

Now YouYou do

Two squares each have sides of 4 in. Are they congruent?

Check whether the size and shape match exactly. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Are two line segments of 8 cm and 8 cm congruent? Yes or no.

  2. 2.Are angles of 40 degrees and 55 degrees congruent? Yes or no.

  3. 3.Congruent figures have the same shape and what else?

On Level

The core Quick Check from the book.

  1. 1.Are two segments of 5 in and 5 in congruent?

  2. 2.Are angles of 90 degrees and 90 degrees congruent?

  3. 3.Are angles of 30 degrees and 60 degrees congruent?

  4. 4.Congruent figures have the same size and what else?

  5. 5.Two rectangles are 3 by 5 and 3 by 6. Are they congruent?

Challenge

Stretch your thinking.

  1. 1.Triangle ABC is congruent to triangle DEF. If side AB is 7 cm, what is the length of its corresponding side DE?

  2. 2.Two squares are congruent. One has a side of 5 in. What is the side length of the other?

  3. 3.A rectangle is 4 by 9 and another is 4 by 9. Are they congruent? Yes or no.