3.1What Are Congruent Figures?

Cade LevinsonPricciHonors Geometry 9

Congruent figures

Part 1: Congruent

• What is Congruent• Congruent figures have all sides and angles

the same size and shape.• Therefore congruent can be defined as any

figure with the same size and shape.• For example…

Look! Flying Pie!Get it Pie! Pi! Math puns!!!

These two triangles have the exact same size and shapes. Congruent triangles need to have all 6 parts (angles + sides) to be equal. This is true with the 2 above triangles. So triangle ABC is congruent to triangle DEF.But…

Does that mean that triangle ABC is also congruent to triangle FED?

NOOOOOO!

The thing is…

• When naming congruent figures, the points have to match up. Since point A is not equal to point F, triangle ABC would not equal Triangle FED.

Polygons reflect!(Pikachu counters!)

• Definition: Congruent polygons have all pairs of corresponding parts congruent.

• Reflections of polygons are congruent since all of their parts are the same size and shape.

• Each reflection also shares a similar part down the middle. Such as…

These Ducks

This leads to the Reflexive Property which states : Any segment or angle is congruent to itself.

Sample Problem

A E

D F

B

C

Given: E and F bisect segments AB and DC respectively. ABCD is a rectangleAre Parallelograms AEFD and EBCF congruentSince E and F bisect the segments those sides are congruent. In a triangle, the opposite sides and angles are congruent . Yes the two figures are congruent.

Practice Problem

• A B

C E F

If E is the midpoint of segment CF, Triangle ACE is congruent to which other triangle?

Triangle BFE

Works Cited

• Rhoad, Richard, Milauskas George, and Whipple Robert. Geometry for Enjoyment and Challenge. Evanston: McDougal, Littell & Company, 1997.

• Feliz, Mike. "Geometry 3.2 Congruent Triangles". Free Math Help. May 15 2008 <http://www.freemathhelp.com/feliz-congruent-triangles.html>.