Download 3.1 What Are Congruent Figures?

Congruent figures
3.1
What Are Congruent Figures?
Cade Levinson
Pricci
Honors Geometry 9
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
B
D
F
C
Given: E and F bisect segments AB and DC respectively. ABCD is a rectangle
Are Parallelograms AEFD and EBCF congruent
Since 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

Triangle BFE







C
 
E

F
If E is the midpoint of segment CF, Triangle
ACE is congruent to which other triangle?
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/felizcongruent-triangles.html>.