Name: ___________________________________________________ Date: _____________________ Block: _______
Unit 4 Congruent Triangles
Apply Triangle Sum Properties
Objectives: I can classify angles and find their measures.
Triangle
A polygon with three sides
Triangle Classification
Equiangular
Acute
Right
Obtuse
By the
ANGLES of a
Triangle
Equilateral
Isosceles
Scalene
By the
SIDES
of a Triangle
Classify the triangle by is sides and angles. You must always be as specific as possible.
A)
B)
Explain why the triangle is a scalene right triangle.
_______________________________________________
_______________________________________________
C)
Name: ___________________________________________________ Date: _____________________ Block: _______
Interior Angles
Angle inside the triangle
Exterior Angles
Angles outside the triangle, formed by
extending the sides of the triangle.
Triangle Angle Sum
Theorem
Triangle Exterior Angle
Theorem
A) m1 = _____
B) mZ = _____
C) x = _____, y = _____, z = _____
X
53
Y
Z
Find the value of x and the mB.
The variable expressions represent the angle measure of a triangle. Find the measure of each angle.
mA  6x  11
mB  3x  2
mC  5x  1
Name: ___________________________________________________ Date: _____________________ Block: _______
Isosceles Triangle Properties
Objectives:
1) Use properties of isosceles and equilateral triangles.
2) Use properties of right triangles.
Isosceles Triangle
Legs
Vertex angle
Base
Base angles
Triangle with at least two sides congruent.
Congruent sides
Angle where the two legs meet
Third side of the triangle (Opposite the vertex angle)
Angles created by the legs and the base
Isosceles Triangle
Theorem
Converse
Isosceles Triangle
Theorem
Corollaries
Use the diagram to fill in the blanks. Tell what theorem you used.
̅̅̅̅ ≅ ̅̅̅̅
A) If𝐴𝐸
𝐷𝐸 , then ______  ______. Theorem or Converse
B) If EDC  CED, then ______  ______. Theorem or Converse
̅̅̅̅ ≅ ̅̅̅̅
C) If𝐴𝐵
𝐸𝐵, then ______  _______. Theorem or Converse
D) If EBC  ECB, then _______  ______. Theorem or Converse
Using the Isosceles Triangle Theorem or the Converse Isosceles Triangle Theorem, find the value of x and y and z.
A)
B)
C)
D)
3z + 2
8z - 33
Name: ___________________________________________________ Date: _____________________ Block: _______
Congruence and Triangles
Objective: Identify congruent figures and corresponding parts
Congruent Triangles
Corresponding Parts
Third Angle Theorem
Write a congruence statement for the triangles. Identify all pairs of congruent corresponding parts.
Congruence Statement: ____________  ____________
Corresponding angles:
Corresponding sides:
Given ABC  DEF, label the diagram. Then, identify all pairs of congruent corresponding parts.
Corresponding angles:
Corresponding sides:
Given that MKL  JET, complete each statement.
A) L  ___________
B) MK  _______________
C) mE = _________
D) ML = _______________
E) ETJ  _________
F) JTE  _____________
Find the value of x.
A)
B)
Name: ___________________________________________________ Date: _____________________ Block: _______
Properties of Congruent Triangles
Can the following triangles be proved congruent? If so, write a congruence statement. Explain your reasoning.
A)
B)
C)
D)
Proving Triangles are Congruent: SSS, SAS, and HL
Notes
Objectives: Prove that triangles are congruent using the SSS Congruence Postulate and the SAS Congruence Theorem.
Side Side Side
Congruence
(SSS)
Decide whether the congruence statement is true.
A)
B)
C)
Name: ___________________________________________________ Date: _____________________ Block: _______
Fill in the following proofs with the necessary Statements and Reasons to prove the triangles congruent.
A)
B)
Statements
Reason
Statements
Reason
Side Angle Side
Congruence
SAS
Included Angle
Hypotenuse Leg
Congruence
HL
Use the diagram to name the included angle between the pair of sides.
A)
B)
C)
Name: ___________________________________________________ Date: _____________________ Block: _______
Decide whether the congruence statement is true.
A)
B)
C)
Given: O is the midpoint of MQ
O is the midpoint of NP
Prove:
Statements
Reasons
Name: ___________________________________________________ Date: _____________________ Block: _______
Statements
Reason
Name: ___________________________________________________ Date: _____________________ Block: _______
Proving Triangles Congruent: ASA, AAS
__________
_
Objectives: Prove that triangles are congruent using the ASA Congruence Postulate and the AAS Congruence Theorem.
Angle Side Angle
Congruence
ASA
Included Side
Angle Angle Side
Congruence
AAS
Is it possible to prove that the triangles are congruent? If so, state the postulate or theorem you would use. Explain
your reasoning.
T
A.
B.
C.
D.
E.
F.
Name: ___________________________________________________ Date: _____________________ Block: _______
Fill in the Proof.
Statements
Reasons
Given: AD || EC
BD  BC
Prove: ∆ ABD  ∆ EBC
Given: B  C
D  F
M is the midpoint of DF.
Prove: ∆ BDM  ∆ CFM
Statements
Reasons
Name: ___________________________________________________ Date: _____________________ Block: _______
Using Congruent Triangles
Objective:
Use congruent triangles to plan and write proofs.
CPCTCCorresponding Parts of
Congruent Triangles are
Congruent
*Explanation: To prove that parts
(sides or angles) of triangles are
congruent to parts of other triangles,
first prove the triangles are
congruent. Then by CPCTC, all
other corresponding parts will be
congruent.
Given: AB  DC ; AD  BC
Prove: A  C
Statements
Reasons
Given: MA  TA , A is the midpoint of SR
Prove: MS  TR
Statements
Reasons
Name: ___________________________________________________ Date: _____________________ Block: _______
Given: 1  2 ; 3  4
Prove: CB  CD
Statements
Reasons
Given: MS || TR; MS  TR
Prove: A is the midpoint of MT.
Statements
Reasons