Download G - 4_1 congruent triangles

Chapter 4
TRIANGLE CONGRUENCY
Warm up – Wednesday (GET OUT REVIEW FROM LAST WEEK)
*Test tomorrow on chapter 3*
There are two ways to classify triangles
By their angles:
Equilateral – all angles congruent
Acute – all angles are acute
Right – one right angle
Obtuse – one obtuse angle
By their sides
Equilateral – all sides are congruent
Isosceles – two sides are congruent
Scalene – no sides are congruent
Classify triangles first by their angles and then by their sides.
1)
2)
4)
3)
5)
What do the angles
in a triangle
add up to?
Warm up – Thursday *make sure you have a PENCIL ready for your test*
**If you have any questions about the homework make sure you ask!**
Warm up – Friday (have any questions from homework out on your desk!)
*if you haven’t gone up to the board you need to do so! *
Find the value of x for which g || h. Prove your steps.
1)
2)
Review from Wednesday:
**remember the triangle angle sum theorem
states that the three angles in a triangle add
up to 180 degrees.
The variable expressions represent the angle measures of the triangle. Find the measure
of each triangle and then classify the triangle by its angles.
1) m
2) m
3) m
A=x
B = 7x
C=x
1) m
2) m
3) m
W = 90 degrees
X = 2x
Y= x
HOMEWORK CHECK! Get out homework from last week and this
week!
Last week Wednesday (Pg 149 #33-44 and #1-8 all)
Last week Thursday (Pg 181 #1-16 all)
This week Wednesday (same as Thursday of last week)
This week Thursday (Pg 186 #1-13, 17-22, and 26-29 all)
** get out piece of paper. NO talking or you will get a zero **
Wed night (last week)
1) #40
2) #4
3) #8 show work
Thurs(last week)/Wed(this week) – it was the same thing!
4) #2
5) #9 show work
6) #14
Last nights homework
7) #4
8) #6 show work
9) #19
10) #22 show work
Warm up – Tuesday **Homework check this week so ask if you need help**
For 1-4. Find the measure of the third angle in the triangle given the
two angles. Then classify the triangle by its angles.
Find the value of x, y and z.
Review from last week:
4.2
CONGRUENCE AND TRIANGLES
Vocabulary from 4-2
When dealing with CONGRUENT figures you have to identify
CORRESPONDING Sides and CORRESPONDING Angles.
1) Corresponding sides – are a pair of congruent sides in two
different figures.
2) Corresponding angles – are a pair of congruent angles in two
different figures.
3) Congruence statement – stating that two shapes are congruent
to each other. MUST PUT THE LETTERS IN THE SAME ORDER!!!
Objective check:
4) Find the value of x and then find
the measure of each angle and
classify the triangle. SHOW WORK!
3) Find the measure of
angle 3 and angle 4.
Warm up – Friday
Find the measure of each missing angle and classify what type of triangle:
1) 2)
2)
3)
4) Given:
a) Find 3 pairs of congruent segments
b) Find 2 pairs of congruent angles.
Challenge: Are they congruent? Justify your answers!
*remember must prove all sides and angles are equal
Review of 4.2 (practicing justifying your answers)
Are the congruent? If they are congruent, then write a congruency statement.
JUSTIFY YOUR ANSWERS!
1)
2)
4.3
PROVING TRIANGLES CONGRUENT BY SSS AND SAS
Ways to prove triangles congruent:
Would you use SSS, SAS, or not enough information for
either? Justify your answers!
Classwork:
Page 216
#2-13
Practice writing proofs:
Warm up – Monday (copy homework and then start warm up)
*Quiz on 4.1 – 4.4 on Thursday – will have proofs on it!*
Find the value of the variables.
1)
2)
3)
Are the congruent. Explain why or why not!
4)
5)
**Go to postulate/theorem section of your notebook**
Warm up – Tuesday (Quiz Thursday!)
A) Name what postulate proves it congruent:
1)
2)
3)
4)
5)
You try:
Writing proofs:
Warm up – Wednesday (quiz tomorrow)
1)
2)
3)
Topics on Quiz
*Congruent shapes and corresponding sides and angles
*Classifying triangles by their angles and sides
*Finding the missing angles of a triangle
*Proofs on SSS, SAS, AAS, and ASA
•
Remember to study angle pairs because they are
often used in proofs.
**We will review a few problems together and then you
will work on a review on your own.
Basic identifications:
State the postulate or theorem that can be used to prove the triangles congruent.
If you cannot prove the triangles congruent, write not enough information.
Practicing proofs: try to start it on your own
Warm up – Monday (Test on Friday, October 30th )
1)
Big mistake on your quizzes:
**If you are using SAS, SSS, AAS, or ASA. You must
have a PAIR of each of those letters in the acronym
in your proof
Ex. If you are proving by AAS…
Your proof must have two pairs of angles and one pair
of sides in your proof!!! You cannot assume I know
what you mean if it is not on your proof!
You will do the same proofs from last week in order
to prove the triangles congruent first.
*SAS, SSS, AAS, ASA*
There will only be one more step to the proof!
New step in the proof – which will be the final step if you are
trying to prove a part of a triangle congruent to another part
of a triangle.
CPCTC (use the acronym)
Corresponding
Parts of
Congruent
Triangles are
Congruent
Proof 2)
Proof 3:
You try:
1)
2)
Warm up – Tuesday (test Friday!)
**if you need help on proofs you need to get help during the warm ups
1) 2)
2)
Warm up – Tuesday (test Friday!)
**if you need help on proofs you need to get help during the warm ups
1) 2)
2)
Objective check from yesterday! Look over it with me!
1)
2)
Practice proof together:
Warm up – Wednesday (Test Friday!)
**Volunteers to put up the answers today**
1)
Section 4.6 – Proving triangles congruent
Review before section 4.6:
Basics on right triangles:
**remember the
hypotenuse is always
across from the
right angle
Review: Basics on isosceles triangles.
Equilateral triangle theorems: (you already know this!)
Hypotenuse-Leg theorem (HL)
If the hypotenuse and a leg of one right triangle is congruent to the
hypotenuse and leg of another right triangle then the triangles are
congruent.
Using equilateral triangles theorem:
1)
2)
Warm up – Thursday – TEST TOMORROW
Using H.L. theorem
Make a proof:
3)
Find the value of x and y
4)
Practice problems of all three:
3)
2)
4)
Solve together:
1)
3) Given:
Prove:
2)