1. Bellwork: 1. Write a two-column proof for the following theorem:
If the angles of a triangle are congruent, then the measure of each angle is 60°.
2. Last summer Mr. Mack built a storage shed in his backyard. The roof of the shed was built using trusses (triangular support) as shown below. Each truss was an isosceles triangle where AB  AC. The length of BC was 4 ft longer than AB. The perimeter of each truss was 28 ft.
What are the lengths for each side of the truss? Show your work in a logical manner and include all calculations.
If Mr. Mack had 110 ft of lumber, how many trusses could he build? Show your work. A B C

2. Unit 4 – Triangle Congruence 4.4 Congruent Triangles
What does it mean for two figures to be congruent?
Corresponding angles and corresponding sides are in the same relative position.
Congruent polygons have congruent corresponding parts.
……and…..
All corresponding angles are congruent.
All corresponding sides are congruent

3. Unit 4 – Triangle Congruence 4.4 Congruent Triangles
When you write a statement such as ABC  DEF, you are also stating which parts are congruent.
You don’t need a diagram to know which parts correspond.
If polygon LMNP  polygon EFGH, identify all pairs of corresponding congruent parts.
Angles: L  E, M  F, N  G, P  H
Sides: LM  EF, MN  FG, NP  GH, LP  EH

4. Unit 4 – Triangle Congruence 4.4 Congruent Triangles
List the corresponding vertices in the same order.
The first polygon can start with any vertex and go in either direction…but then the second polygon is ‘fixed’. B
∆BAC  ∆ ____
∆ABC  ∆ ____ Q T
∆JTQ  ∆ ____ A C J
List the congruent corresponding parts angles
sides

5. Unit 4 – Triangle Congruence 4.4 Congruent Triangles
If polygons are congruent, then corresponding parts are congruent. Find all the angle measures and side lengths for both the following figures if ∆ABC  ∆XYZ A B C
90° 24 X Y Z
30° 20 15

6. Unit 4 – Triangle Congruence 4.4 Congruent Triangles
Find the angle measures and side lengths for the following figures if ∆ABC  ∆EDF
(2x+10)°
4y - 10 2y A B C
50°
3y + 4
60° 12 F D E

7. Unit 4 – Triangle Congruence 4.4 Congruent Triangles
In the figure below, can you show ∆ABC ∆CDE? Justify your answer.

8. Unit 4 – Triangle Congruence 4.4 Congruent Triangles
Given: AD bisects BE.
BE bisects AD.
AB  DE, A  D
Prove: ∆ABC  ∆DEC

9. Given: MP bisects ∡NMR. P is mdpt of NR Prove: ∆MNP≅ ∆MRP
Unit 4 – Triangle Congruence Congruent Triangles M N P R
Given: MP bisects ∡NMR.
P is mdpt of NR
Prove: ∆MNP≅ ∆MRP

10. Unit 4 – Triangle Congruence 4.4 Congruent Triangles
Homework:
4.4(242): 13-20,22,23,31,32,34
14) CF 16) Angle D 18) 19 22) RVUTS = VWXZY 32) x=27,y=20 34)97