Triangle Congruence Criteria in Geometry
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 corres-
ponding 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
C
orresponding
P
arts of
C
ongruent
T
riangles are
C
ongruent)
*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
Equilateral Triangle
Leg Leg
Base
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 F
If BC ≌ EF and AC ≌ DF, then 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)
Explore the concept of congruence criteria for triangles in geometry, including SSS, SAS, ASA Postulates, and AAS Theorem. Learn to identify congruent figures and their corresponding parts, solve problems, and prove relationships in geometric figures. Dive into the principles of congruent polygons, recognizing matching sides and angles. Discover how to prove triangles congruent using different postulates and theorems, which involve specific combinations of sides and angles. Enhance your geometric reasoning and problem-solving skills through engaging examples and visuals.
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Presentation Transcript
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 corres- ponding sides and 3 corresponding s. Corr. Sides 1) 2) 3) A X Corr. Angles 1) 2) 3) 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 Equilateral Triangle Leg Leg Base
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 F If BC EF and AC DF, then 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)
