Download Chapter 4 Notes

Chapter 4.1
Common Core - G.SRT.5 Use congruence…criteria
for triangles to solve problems and prove
relationships in geometric figures.
Objectives – To recognize congruent figures and
their corresponding parts.
Ch 4.1 Notes
Congruent Polygons – have congruent
corresponding parts – their matching side and
angles. When you name congruent polygons,
you must list corresponding vertices in the
same order.
If 2 triangles are ≌ then they have 3 corresponding sides and 3 corresponding ∠’s.
Corr. Sides
Corr. Angles
1)
1)
2)
2)
3)
3)
A
X
B
C
Y
Z
Chapter 4.2
Common Core -G.SRT.5 Use congruence…criteria
for triangles to solve problems and prove
relationships in geometric figures.
Objectives – To prove two triangles congruent
using SSS and SAS Postulates.
Ch 4.2 Notes
Side-Side-Side Post. (SSS) – if 3 sides of one
triangle are ≌ to 3 sides of another triangle,
then the 2 triangles are congruent
≌
Side-Angle-Side Post. (SAS) – if 2 sides and the
included ∠ of one triangle are ≌ to 2 side
and the included angle of a second triangle,
then the 2 triangles are ≌.
≌
Chapter 4.3
Common Core - G.SRT.5 Use congruence…criteria
for triangles to solve problems and prove
relationships in geometric figures.
Objectives – To prove two triangles congruent
using ASA Postulate and AAS Theorem.
Ch 4.3 Notes
Angle-Side-Angle Post. (ASA) – if 2 ∠’s and the
included side of one triangle are ≌ to 2 ∠’s and the
included side of a second triangle, then the 2
triangles are congruent
≌
Angle-Angle-Side Post. (AAS) – if 2 ∠’s and a
nonincluded side of one triangle are ≌ to 2 ∠’s
and the corresponding nonincluded side of a
second triangle, then the 2 triangles are ≌.
≌
Chapter 4.4
Common Core - G.SRT.5 & G.CO.12 Use
congruence…criteria for triangles to solve problems
and prove relationships in geometric figures.
Objectives – To use triangle congruence and
corresponding parts of congruent triangles to
prove that parts of two triangles are congruent.
Ch 4.4 Notes
Once you have 2 triangles ≌ then you can
say anything you want about their
corresponding parts.
(It is called Corresponding Parts of
Congruent Triangles are Congruent)
*You can use the acronym C.P.C.T.C
Chapter 4.5
Common Core Common Core - G.CO.10, G.CO.13
& G.SRT.5 Prove theorems about triangles…base
angles of isosceles triangles are congruent.
Objectives – To use and apply properties of
isosceles and equilateral triangles.
Ch 4.5 Notes
Isosceles Triangle
Leg
Leg
Base
Equilateral Triangle
Base Angle Thm – if 2 sides of a triangle are ≌,
then the angles opposite them are ≌.
If
then
If AB ≌ AC, the ∠B ≌ ∠C
Converse of the Base Angles Thm – If 2 ∠’s of a
triangle are ≌, then the sides opposite them
are ≌.
If
then
If a line bisects the vertex angle of an isosceles
triangle, then the line is also the perpendicular
bisector of the base.
If
then
Corollaries
If a triangle is equilateral, then it is equiangular.
If
then
If a triangle is equiangular, then it is equilateral.
If
then
Chapter 4.6
Common Core – G.SRT.5 Use congruence…criteria
to solve problems and prove relationships in
geometric figures.
Objective – To prove right triangles congruent
suing the Hypotenuse-Leg Theorem.
Ch 4.6 Notes
Hypotenuse-Leg Congruence Thm (HL)
If the hypotenuse and a leg of a right triangle
are ≌ to the hypotenuse and a leg of a
second right triangle, then the 2 triangles
are ≌.
A
D
B
C
E
If BC ≌ EF and AC ≌ DF, then
F
ABC ≌
DEF
Chapter 4.7
Common Core – G.SRT.5 Use congruence…criteria
to solve problems and prove relationships in
geometric figures.
Objectives – To identify congruent overlapping
triangles. To prove two triangles congruent using
other congruent triangles.
Ch 4.7 Notes
Congruence in Overlapping Triangles - You can
sometimes use the congruent corresponding
parts of one pair of congruent triangles to
prove another pair of triangles congruent.
Review the five way to prove
to two triangles congruent.
1)
2)
3)
4)
5)