Download of your Geometry Textbook

Name_________________________
Unit 4.1 – Triangles
1) Go to flippedmath.com
Click here and
select
MyGeometry
2) Click on Semester 1
Unit 4
Open the MyGeometry course
DoDEA Geometry Standard
G.2: Triangles
Students identify and describe various kinds of
triangles (right, acute, scalene, isosceles, etc.) They
prove that triangles are congruent or similar and use
properties of these triangles to solve problems.
G.1.1: Demonstrate understanding by identifying and
giving examples of undefined terms, axioms,
theorems, and inductive and deductive reasoning
Section 4.1
Watch video entitled
“Triangles”
READ pages 218 - 220
and 250-252
of your Geometry Textbook
The flippedmath.com video corresponds to the information presented in
this section of your textbook.
3) HOMEWORK: Complete Unit 4.1
NO LATER THAN Dec 10
You have class time to complete the video, take notes, and start the
practice and applications. There is also time for asking questions and
clarifying concepts on an individual basis.
USE THIS TIME WISELY TO BE SUCCESSFUL!!! Stay on task.
REMEMBER: In addition to reading your text (pages 218-220 and 250252) you can open your online textbook and view the publisher’s
lesson videos in your student resources
E-mail if you have any questions: [email protected]
4.1 Triangles and Congruent Figures
NOTES
Write your
questions here!
ACUTE
Types of triangles
OBTUSE
RIGHT
SCALENE
ISOSCELES
EQUILATERAL
Isosceles Triangle Theorem
If…
Then…
Theorem
If two sides of a triangle
are congruent, then
Theorem
Converse of the Isosceles Triangle Theorem
If…
Then…
If two angles of a triangle
are congruent, then
Write your
questions here!
Equilateral Triangle Theorem
If…
Then…
Theorem
If a triangle is equilateral,
then
Theorem
Converse of the Equilateral Triangle Theorem
If…
Then…
If a triangle is equiangular,
then
Congruent FiguresCorresponding PartsExample #1
Try it!
Example #2
Summarize your notes:
Now,
summarize
your notes
here!
4.1 PRACTICE
Draw the following. Mark the picture!!!
1. Obtuse Isosceles Triangle
2. Acute Equilateral Triangle
3. Right Scalene Triangle
Find x.
4.
5.
6.
7.
8.
9.
Mark the angles and sides of each pair of triangles to indicate that they are congruent.
10.
11.
12.
Write a statement indicating that the triangle pair is congruent. ORDER IS IMPORTANT!!!
13.
14.
15.
Complete each congruence statement.
16.
17.
SOLVE
2(3𝑥 − 4) − 5 = −7
SOLVE
𝑥 𝑥+2
=
5
15
𝑦=
3
𝑥
4
18.
ALGEBRA REVIEW
GRAPH
GRAPH
𝑦=𝑥
MULTIPLY
(2𝑥 − 3)(𝑥 + 3)
FACTOR
𝑥 − 4𝑥 − 12
2
4.1 APPLICATION
2. Given ∠𝑇 = 𝑥 2 and ∠𝐼 = 3𝑥 + 18. Find x.
1. Mark the picture.
Watch the application walk through video if you need extra help getting started!
In order to prove that two triangles are congruent, you must show that every
corresponding angle and every corresponding side is congruent.
3. Mark the picture and then prove it. Show ALL SIDES and ALL ANGLES ≅ !!!
���� ∥ ����
Given: 𝑮𝑰
𝑻𝑹
����
H is the midpoint of 𝑮𝑻
���� ≅ 𝑹𝑻
����
𝑮𝑰
����� ≅ ����
𝑯𝑹
𝑰𝑯
Prove: ∆𝑮𝑯𝑰 ≅ ∆𝑻𝑯𝑹
STATEMENTS
��� ∥ 𝑇𝑅
����
1. 𝐺𝐼
����
H is the midpoint of 𝐺𝑇
��� ≅ ����
𝐺𝐼
𝑅𝑇
����
���
𝐻𝑅 ≅ �𝐼𝐻
REASONS
1.
���� ≅ 𝐻𝑇
����
2. 𝐺𝐻
2.
4. ∠𝐼 ≅ ∠𝑅
4.
3. ∠𝐺 ≅ ∠𝑇
3. Alternate Interior Angles are congruent
5.
5.
6. ∆𝐺𝐻𝐼 ≅ ∆𝑇𝐻𝑅
6. Definition of Congruent Triangles
4. Mark the picture and then prove it. Show ALL SIDES and ALL ANGLES ≅ !!!
�����
Given: ∆𝑽𝑿𝑾 is an isosceles triangle with base 𝑽𝑾
���� is an angle bisector of ∠𝑽𝑿𝑾
𝑿𝑷
�����
P is the midpoint of 𝑽𝑾
∠𝑽𝑷𝑿 ≅ ∠𝑾𝑷𝑿
Prove: ∆𝑷𝑽𝑿 ≅ ∆𝑷𝑾𝑿
STATEMENTS
1. ∆𝑉𝑋𝑊 is an isosceles triangle
����
𝑋𝑃 is an angle bisector of ∠𝑉𝑋𝑊
�����
P is the midpoint of 𝑉𝑊
∠𝑉𝑃𝑋 ≅ ∠𝑊𝑃𝑋
REASONS
1.
���� ≅ 𝑋𝑃
����
2. 𝑋𝑃
2.
���� ≅ 𝑋𝑊
�����
3. 𝑉𝑋
3.
4.
4.
5. ∠𝑉𝑋𝑃 ≅ ∠𝑊𝑋𝑃
5.
7. ∆𝑃𝑉𝑋 ≅ ∆𝑃𝑊𝑋
7.
6. ∠𝑋𝑉𝑃 ≅ ∠𝑋𝑊𝑃
6.
5. Fill in the measure of every angle:
GIVEN:
Name any isosceles triangles.