Unit 4: Day 1

Reminders Vocabulary Quiz on Wednesday

Warm Up Journal Draw an acute triangle. Label the angle measures. Draw a right triangle. Label the angle measures. Draw an obtuse triangle. Label the angle measures. #1 How many acute angles does an acute triangle have? #2 How many acute & obtuse angles does a right triangle have? #3 How many obtuse angles does an obtuse angle have? In 2-3 sentences, describe everything you know about triangles.

Assignment Sheet DateAssignmentGrade Warm Up & Journals 11/7Unit 4 Vocabulary 11/10Triangle Notes Day 1 11/10 Classifying Triangles WKST 11/11Triangle Notes Day 2 11/11Triangle Sum Theorem WKST

Header: Triangle Notes Day 1 Use your formatting math notes Star Key Concepts Underline Key terms Box Theorems

Classifying Triangles Scalene Triangle None of the sides and none of the angles are the same.

Isosceles Triangle Which type of triangle is this? Two sides and two angles are the same.

Which type of triangle is this? Equilateral Triangle All sides and all angles are the same.

Day 2

Header: Triangle Notes Day 2 Use your formatting math notes Star Key Concepts Underline Key terms Box Theorems

Assignment Sheet DateAssignmentGrade Warm Up & Journals 11/7Unit 4 Vocabulary 11/10Triangle Notes Day 1 11/10 Classifying Triangles WKST 11/11Triangle Notes Day 2 11/11Triangle Sum Theorem WKST

Review Classifying Triangles Scalene Triangle None of the sides and none of the angles are the same.

Isosceles Triangle Review Classifying Triangles Two sides and two angles are the same.

Review Classifying Triangles Equilateral Triangle All sides and all angles are the same.

Corollaries What's a corollary? If a triangle is equilateral, then it must be equiangular.

Corollaries If a triangle is equiangular, then it must be equilateral.

Practice A B C

A B C Opposite Sides & Angles

A B D C

Day 3

KEY CONCEPT!!!!

Practice

How do we know our answer is correct?

Practice

How do we know our answer is correct?

Find the degree measure of the interior angles of triangle ABC. Practice

Day 4

Assignment Sheet DateAssignmentGrade Warm Up & Journals 11/7Unit 4 Vocabulary 11/10Triangle Notes Day 1 11/10 Classifying Triangles WKST 11/11Triangle Notes Day 2 11/11Triangle Sum Theorem WKST 11/12Triangle Notes Day 3 11/13Triangle Notes Day 4 11/13Exterior Angles Worksheet

Warm Up Journal Find the slope of a line 1. F (2,5) B (-2,3) 2. A(0,-5) D (2,0) 3. E(1,1) F(2,-4) Explain how to find the measure of an angle in a triangle, when two other angles are known.

Homework Review

Label Your Notes: Triangle Notes Day 4 Use your math notes cheat sheet to help you take good notes today and follow my directions First key concept…..Exterior Angles Put a big star on your notes and write Exterior Angles

Find the missing angle measure. x Practice

Find the missing angle measures. Practice

Which type of triangle is this? Acute Isosceles

9 CM 7 CM 11 CM Which type of triangle is this? Right Scalene

Triangle Exterior Angle Conjecture- The measure of the exterior angle of a triangle is… equal to the sum of the measures of the two nonadjacent interior angles. The angles circled in red are nonadjacent interior angles for x.

Day 5

Warm Up Journal Work on Vocabulary Terms Describe the six ways to classify a triangle.

Assignment Sheet DateAssignmentGrade Warm Up & Journals 11/7 Unit 4 Vocabulary 11/10 Triangle Notes Day 1 11/10 Classifying Triangles WKST 11/11 Triangle Notes Day 2 11/11 Triangle Sum Theorem WKST 11/12 Triangle Notes Day 3 11/13 Triangle Notes Day 4 11/13 Exterior Angles Worksheet 11/14 Unit 4 Vocab Quiz #1 11/14 Triangle Notes Day 5 11/14 Corresponding Angles Wkst

Solve for x and y. Practice

Congruent Triangles Congruent Triangles: When two triangles are the exact same size and shape they are said to be congruent. Even though they have the same shape and size, they may be positioned differently.

What corresponding parts of the two congruent triangles are congruent? a b c z y x

a b c z y x This slide demonstrates the concept of CPCTC. If two triangles are congruent, then the corresponding parts of those congruent triangles are congruent.

Are the lines given by the following equations perpendicular, parallel, or neither? Review Perpendicular

Are the lines given by the following equations perpendicular, parallel, or neither? Review Parallel

Are the lines given by the following equations perpendicular, parallel, or neither? Review Neither

Are the lines given by the following equations perpendicular, parallel, or neither? Review Perpendicular

Congruent Triangles Third Angle Theorem: If two angles of one triangle are congruent to two angles of another triangle, then the third angle must also be congruent.

Isosceles Triangles Isosceles Triangle Conjecture: An isosceles triangle has two congruent angles. The sides opposite the congruent angles(legs) are also congruent. Vertex Angle

Isosceles Triangles Converse of the Isosceles Triangle Conjecture: A triangle that has two congruent angles must be isosceles. If a triangle has two congruent sides, then it is isosceles. Vertex Angle

Isosceles Triangles Vertex Angle: Angle between the two congruent sides. Legs: Congruent sides. Base Base Angle

Base Angles Theorem If two sides of a triangle are congruent, then the angles opposite them are congruent. D E F

Converse of the Base Angles Theorem If two angles of a triangle are congruent, then the sides opposite them are congruent. D E F

Practice A B C

D E C

23 Practice

By comparing only three parts of two different triangles we will try to determine if the two triangles are congruent. Basically, we will try to answer the following question: Is ?

You have already seen that if two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. Which conjecture tells you this? The Third Angle Conjecture 60 ̊ 90 ̊ 30 ̊

Just what is this congruence you speak of? a b c z y x S A S

Side-Side-Side (SSS) Congruence Postulate: If three sides in one triangle are congruent to corresponding sides in another triangle, then the triangles are congruent. s t w d e h How do we indicate their congruence?

Side-Angle-Side (SAS) Congruence Postulate: If corresponding sides and the included angle (angle between the two congruent sides) are congruent in two triangles, then the triangles are congruent. z y x w t s How do we indicate their congruence?

Angle-Side-Angle (ASA) Congruence Postulate: If corresponding angles and the included side (the side between the angles) are congruent in two triangles, then the triangles are congruent. a b c How do we indicate their congruence? z x y

Side-Angle-Angle (SAA) Congruence Theorem: If corresponding angles and a non-included side of two triangles are congruent, then the triangles are congruent. a b c How do we indicate their congruence? z x y

Hypotenuse-Leg (HL) Congruence Theorem: If the hypotenuse and a corresponding leg of two right triangles are congruent, then the triangles are congruent. How do we indicate their congruence? A B C D E F

Side-Side-Angle (SSA) Congruence Conjecture: If corresponding sides and a non-included angle of two triangles are congruent, then the triangles are congruent. a b c z x y not enough by itself

Angle-Angle-Angle (AAA) Congruence Conjecture: If two triangles have all congruent angles, then the triangles are congruent. not enough by itself

Triangle Notes Day 4 Reminders: Test Friday Mrs. Warren out Thursday

Assignment Sheet DateAssignmentGrade Signature 2/11Cumulative Review #1 Due____/___ 2/13Corresponding Parts Wkst 2/14Vocab Quiz #1 2/14Triangle Notes Day 3 2/14Isosceles Wkst 2/14Congruence Wkst 2/18Triangle Proof Notes 2/18Congruence Wkst #2 2/18Unit 3 Quiz #1 2/19Study Guide

Warm Up Journal Describe the 5 ways to prove triangle congruence.

Are the two triangles congruent? If so, how do you know? SAS

Are the two triangles congruent? If so, how do you know? SSS

Are the two triangles congruent? If so, how do you know? Not Enough Information

Are the two triangles congruent? If so, how do you know? SAS

Are the two triangles congruent? If so, how do you know? SSS

Are the two triangles congruent? If so, how do you know? AAS

Are the two triangles congruent? If so, how do you know? AAS

Are the two triangles congruent? If so, how do you know? ASA

Are the two triangles congruent? If so, how do you know? HLT

Are the two triangles congruent? If so, how do you know? SAA

Are the two triangles congruent? If so, how do you know? SAS

Practice For the following slides, complete the two column proofs.

Statements Reasons A B C 1. Given 2. Given 3. Reflexive property 4. SAS 5. CPCTC D

Q P R S Statements Reasons 1. Given 2. Given 3. Reflexive property 4. SSS 5. CPCTC

A D B E 1. Given 2. Reflexive property 4. AAS 5. CPCTC Statements Reasons

Practice For the following slides, complete the two column or flow chart proofs.

Statements Reasons Prove that the two triangles are congruent a b cd 2. Reflexive property 4. ASA 1. Given Practice

r n c o Statements Reasons w 2. Vertical Angles Theorem 3. SAS 4. CPCTC 1. Given

A B C D E

Flow Chart a b c d e f Given AAS CPCTC

a b c d Given Definition of an altitude Reflexive Property SAS CPCTC

Statements Reasons A BCD Definition of a midpoint Given Reflexive Property SSS CPCTC

Prove angle B is congruent to angle D. Statements Reasons A BC D

X YZ W 3. Reflexive Property 4. HLT 1. Given Statements Reasons 5. CPCTC

Bisectors of a Triangle A B C D Any point on the perpendicular bisector of a segment must be equidistant from the endpoints of the segment.

A F B E D C Bisectors of a Triangle Concurrency of Perpendicular Bisectors of a Triangle: Perpendicular bisectors of a triangle are all concurrent at a point called the circumcenter. This point is equidistant from the all the vertices in the triangle. G

Median A median goes from a vertex in a triangle to the midpoint of the opposite side. A F B E G D C

Median What are the medians in this triangle? A F B E G D C

Median The three medians of a triangle are all concurrent at a point called the centroid. A F B E G D C

Concurrency of Medians of a Triangle The centroid is located at two thirds of the distance from each vertex to the midpoint to the opposite side. A F B E G D C

A F B E G D C

Altitude An altitude in a triangle goes from a vertex and creates a right angle (is perpendicular with) the opposite side. An altitude can lie in, on, or outside the triangle. A B C D

All of the altitudes in a triangle are concurrent at a single point called the orthocenter. Altitude

Midsegment: segment connecting midpoints of two sides of a triangle. A B C D E G

A B C D E G

A B C D E F Practice

135 ̊ 110 ̊ z 77 ̊ 62 ̊ y x 44 ̊ x

5.5 Theorem 5.10 Side-Angle Inequality Theorem: The longest side in a triangle is opposite the largest angle. The shortest side in a triangle is opposite the smallest angle. The side with length in between the lengths of the other sides is opposite the angle that has degree measure in between the other angles. 3cm 4cm 5cm

Side-Angle Inequality A B C List the sides in order from longest to shortest.

Triangle Inequality: The sum of the length of two sides of a triangle must be greater than the length of the third side. A B C 10cm 8cm 17cm

Triangle Inequality: The sum of the length of two sides of a triangle must be greater than the length of the third side. A B C 10cm 8cm 20cm

Determine whether it is possible to draw a triangle with the sides of the given measurements. 8cm, 11cm, 18.5cm 7cm, 17cm, 10.5cm 9cm, 6cm, 19cm How do you know? No Yes No Practice

Hinge Theorem A B C D E F

A B C D E F Practice Fill in the blank with a “less than”, “greater than”, or “equal to” symbol.