Download congruent

C ONGRUENT F IGURES

If you can flip, rotate, or move one
shape to fit exactly on another, the
shapes are congruent.

Two figures are congruent if they
are the same size and shape.
C ONGRUENT VS N OT C ONGRUENT
The two shapes to the
right are congruent:
The two shapes to the
right are NOT congruent:
Corresponding Parts
By Definition if all six pairs of corresponding
parts (sides and angles) are congruent, then
the triangles are congruent.
1. AB ≅ DE
2. BC ≅ EF
3. AC ≅ DF
4. ∠ A ≅ ∠ D
5. ∠ B ≅ ∠ E
6. ∠ C ≅ ∠ F
∆ABC ≅ ∆ DEF
Do you need all six ?
NO !
SSS
SAS
ASA
AAS
R ULES FOR C ONGRUENT
T RIANGLES
SSS – Side, Side, Side Rule
If the three sides of a
triangle are congruent
to the three sides of
another triangle, then
the two triangles are
congruent.
R ULES FOR C ONGRUENT
T RIANGLES
SAS – Side Angle Side Rule
If two sides and the included
angle of a triangle are
congruent to two sides and
the included angle of
another triangle, then the
two triangles are congruent.
Included angle = angle
created by two sides of a
triangle.
R ULES FOR C ONGRUENT
T RIANGLES
ASA – Angle Side Angle Rule
If two angles and the
included side of one triangle
are congruent to two angles
and the included side of
another triangle, then these
two triangles are congruent.
Included side = a side that is
common between two
angles.
R ULES FOR C ONGRUENT
T RIANGLES
AAS – Angle Angle Side
If two angles and a non-
included side of a triangle
are congruent to two
angles and the
corresponding nonincluded side of another
triangle, then the two
triangles are congruent.
Example
R ULES FOR C ONGRUENT
T RIANGLES
HYPOTENUSE-LEG

This rule can only be used with
right triangles (triangles that
have one angle measuring 90°).
It states if the hypotenuse and a
leg of one right triangle are
congruent to the hypotenuse
and a leg of another right
triangle, then the triangles are
congruent.
S IMILAR F IGURES
Two shapes are similar if their corresponding
angles are equal and their corresponding line
segments are proportional.
S IMILAR F IGURES
Here are two similar shapes. Make a statement about the corresponding
angles, using a vocabulary word from today’s lesson in the chat box.
Are these figures similar?
Example 1
If we have a triangle with side lengths of 2, 3, and 4 and a
larger similar triangle with the shortest side equal to 6, what
is the length of the other two sides of the triangle?
x
n
4
3
2
6
Example 1: If we have a triangle with side
lengths of 2, 3, and 4 and a larger similar
triangle with the shortest side equal to 6, what
is the length of the other two sides of the
triangle?
4
3
2
x
n
6
Solution: Since the shortest side of the first
triangle is 2, we know that 2 x 3 is 6, so the
other sides are 3 times the sides of the first
triangle. The other two sides are 9 and 12 (3 x 3
= 9 and 4 x 3 = 12).