Download included angle

5.6 - SSS SAS HL Part 1
Obj: Proving Triangle Congruence by
Side-Side-Side (SSS), Side Angle Side (SAS), and
Hypotenuse Leg (HL).
Warmup:
ΔHIJ ≅ ΔKLM; find all of the missing sides and
angles.
57o
87o
22
18
15
Definitions
An included angle is the
angle between two given
sides
An included side is the
side between two given
angles
Side-Side-Side (SSS)
Congruence
The 3 sides of the first
triangle are congruent to
the 3 sides of the second
triangle
Side-Angle-Side Congruence (SAS)
The 2 sides & included angle of one triangle are
congruent to the 2 sides & included angle of the
second triangle.
Another way to think about this is to consider three
pieces of spaghetti of various lengths. There is only
one triangle that can be made with the three
pieces. Because of this, if I have three other pieces
of spaghetti the same lengths as my original three,
there again will be only one triangle that can be
made. Thus, triangles one and two are congruent.
The same is true for two pieces of spaghetti and a set
included angle for side-angle-side.
Triangle congruence statement. When you
state two triangles to be congruent
(ΔABC ≅ ΔDEF),
you want to check that each of the following
six congruence statements are true.
∠A≅∠D
∠B≅∠E
∠C≅∠F
𝐴𝐵 ≅ 𝐷𝐸
𝐵𝐶 ≅ 𝐸𝐹
𝐴𝐶 ≅ 𝐷𝐹
Examples: Determine if the triangles are
congruent. How do you know?
More Examples