Big Idea: Prove Triangles are Congruent by SAS and HL.
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Transcript of Big Idea: Prove Triangles are Congruent by SAS and HL.
GEOMETRY 10/22/14 BELLWORK
GEOMETRY 4.4
Big Idea: Prove Triangles are Congruent by SAS
and HL
Postulate 20 Side-Angle-Side (SAS) Congruence TheoremIf two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.
R
S
T U
V
W
If Side
Angle
Side
then
Hypotenuse
Leg
Leg
Review: Parts of a right triangle
Theorem 4.5 Hypotenuse-Leg (HL) Congruence TheoremIf the hypotenuse and leg of a right triangle are congruent to the hypotenuse and leg of a second right triangle, then the two triangles are congruent.
A
BC F
D
E
Consider a relationship involving two sides, and the angle they form, their included angle.
Any time you form an angle of the same measure with the pencils, the side formed by connecting the pencil points will have the same length. In fact, any two triangles formed in this way are congruent.
Name the included angle for the following pairs of sides. and
and
and
and
and
ADB
Examples 1 to 5
Determine whether or not the triangles are congruent. Explain your reasoning. Write a
congruence statement if they are congruent.
Example 6
Determine whether or not the triangles are congruent. Explain your reasoning. Write a
congruence statement if they are congruent.
Example 6
Use the given information to name two triangles that are congruent.
Explain your reasoning.
Geometry 10/22/14Bellwork5 min. Q & A on HW
(Finish tomorrow)Textbook: Page 243-244 Exercises: 4-12 Even, 16-22 Even