Discovering Geometry Chapter 4 Test Review HGSH

Slides:

Advertisements

Similar presentations

Chapter 4: Congruent Triangles

Advertisements

1.1 Statements and Reasoning

Congruent Triangles Geometry Chapter 4.

$100 $200 $300 $400 $500 $200 $300 $400 $500 Classifying Triangles Proving Congruence Coordinate Proof Congruence in Right Triangles Isosceles Triangles.

Draw the following: 1. acute triangle 2.right triangle 3.obtuse triangle 4. acute, scalene triangle 5.obtuse, isosceles triangle 6. right, scalene.

Properties and Theorems

Chapter 5: Inequalities!

4-7 Median, Altitude, and Perpendicular bisectors.

JRLeon Discovering Geometry Chapter 4.8 HGSH C H A P T E R 4.8 O B J E C T I V E S  Discover properties of the base angles and the vertex angle bisector.

Basic Definitions in Geometry

Menu Select the class required then click mouse key to view class.

Unit 2 Triangles Triangle Inequalities and Isosceles Triangles.

Triangle Fundamentals

 T RIANGLE : A figure formed by three noncollinear points, connected by segments  Since two of the segments create a vertex, a triangle has three vertices.

Fall 2012 Geometry Exam Review. Chapter 1-5 Review p ProblemsAnswers 1One 2a.Yes, skew b.No 3If you enjoy winter weather, then you are a member.

Isosceles Triangles Geometry D – Chapter 4.6. Definitions - Review Define an isosceles triangle. A triangle with two congruent sides. Name the parts of.

4.5 - Isosceles and Equilateral Triangles. Isosceles Triangles The congruent sides of an isosceles triangles are called it legs. The third side is the.

4.6 Isosceles Triangles.

Aim: Isosceles Triangle Course: Applied Geometry Aim: What is an Isosceles Triangle? Do Now: What type of triangle has sides of 3, 6, 8?

4.5 Isosceles and Equilateral Triangles. Isosceles Triangles At least two sides are of equal length. It also has two congruent angles. Base Angles Base.

1 4-5 Isosceles and Equilateral Triangles State and apply the Isosceles Triangle Theorem and its converse State and apply the corollaries for equilateral.

4.5: Isosceles and Equilateral Triangles Objective: To use and apply properties of isosceles and equilateral triangles.

4.7 Use Isosceles & Equilateral Triangles

4-9 Isosceles and Equilateral Triangles

1. Given right triangle  ABC with angle measures as indicated in the figure. Find x and y. § 21.1 Angles x and z will be complementary to 43 and y will.

Chapter 5 Review Perpendicular Bisector, Angle Bisector, Median, Altitude, Exterior Angles and Inequality.

Stephanie Lalos. Theorem 50 The sum of measures of the three angles of a triangle is 180 o A B C o.

Introduction to Geometry

Chapter 4 Triangle Congruence By: Maya Richards 5 th Period Geometry.

1 Triangle Angle Sum Theorem The sum of the measures of the angles of a triangle is 180°. m ∠A + m ∠B + m ∠C = 180 A B C Ex: If m ∠A = 30 and m∠B = 70;

Basics of Euclidean Geometry Point Line Number line Segment Ray Plane Coordinate plane One letter names a point Two letters names a line, segment, or ray.

Triangle Fundamentals

Unit 5 Notes Triangle Properties. Definitions Classify Triangles by Sides.

4.1 Triangles and Angles. 2 Standard/Objectives: Objectives: Classify triangles by their sides and angles. Find angle measures in triangles DEFINITION:

Triangle Properties - Ch 4 Triangle Sum Conjecture The sum of the measures of the angles of a triangle is…. …180 degrees. C-17 p. 199.

POINTS, LINES AND PLANES Learning Target 5D I can read and write two column proofs involving Triangle Congruence. Geometry 5-3, 5-5 & 5-6 Proving Triangles.

Chapter 9 Parallel Lines

SPECIAL SEGMENTS IN TRIANGLES KEYSTONE GEOMETRY. 2 SPECIAL SEGMENTS OF A TRIANGLE: MEDIAN Definition of a Median: A segment from the vertex of the triangle.

Unit 4: Day 1. Reminders Vocabulary Quiz on Wednesday.

Chapter 4 Ms. Cuervo. Vocabulary: Congruent -Two figures that have the same size and shape. -Two triangles are congruent if and only if their vertices.

October 8,  As we discussed in a previous section isosceles triangles are triangles with at least two sides congruent.  The two congruent sides.

Applied Geometry Lesson: 6 – 4 Isosceles Triangles Objective: Learn to identify and use properties of isosceles triangles.

Pythagorean Theorem Theorem. a² + b² = c² a b c p. 20.

Chapter 4 Review Cut-n-Paste Proofs. StatementsReasons SAS Postulate X is midpoint of AC Definition of Midpoint Given Vertical Angles Theorem X is midpoint.

A triangle in which exactly one angle is obtuse is called an ___________ triangle.

EXAMPLE 3 Find the orthocenter Find the orthocenter P in an acute, a right, and an obtuse triangle. SOLUTION Acute triangle P is inside triangle. Right.

How to use and apply properties of isosceles triangles. Chapter 4.5GeometryStandard/Goal: 4.1.

Triangle Inequalities Objectives: 1.Discover inequalities among sides and angles in triangles.

1. Prove that the three angle bisectors of a triangle concur. C AB D F E I § 4.1.

Geometry SOL review Session 2. Triangle relationships Congruent triangles Similar triangles Right triangles Triangle inequalities.

Triangles and Their Angles Geometry – Section 4.1.

Triangle Fundamentals

5.4 Isosceles and Equilateral Triangles

Triangle Fundamentals

3.5 Parallel Lines and Triangles

Pearson Unit 1 Topic 4: Congruent Triangles 4-5: Isosceles and Equilateral Triangles Pearson Texas Geometry ©2016 Holt Geometry Texas ©2007.

Triangle Fundamentals

Triangles A polygon with 3 sides.

4.1 Triangles and Angles.

Triangle Fundamentals

Congruent Triangles 4-1: Classifying Triangles

4.5 - Isosceles and Equilateral Triangles

Triangle Fundamentals

MID-TERM STUFF HONORS GEOMETRY.

Joianna Wallace Pd:1 Extra Credit

4.6 Isosceles Triangles.

G9 - Congruence Postulates for Triangles

Naming Triangles Triangles are named by using its vertices.

5-7 Isosceles and Equilateral Triangles

Presentation transcript:

Discovering Geometry Chapter 4 Test Review HGSH

Discovering Geometry Chapter 4 Test Review HGSH 1 2 3 1 and 2 are Vertical Angles. 3 and 4 are Alternate Interior Angles and are equal by the Parallel Line Conjecture. Discovering Geometry Chapter 4 Test Review HGSH

Discovering Geometry Chapter 4 Test Review HGSH BC = (8X +3) YZ = (7X +5) Because of the way the triangle congruence is written A and X are corresponding angles C and Z are corresponding angles BC and YZ are corresponding, So: BC = YZ 8x + 3 = 7x + 5 , subtract 7x x+3 = 5 , subtract 3 x=2 Discovering Geometry Chapter 4 Test Review HGSH

Discovering Geometry Chapter 4 Test Review HGSH Triangle Sum Conjecture B = 180° – (60° + 45°) B = 75° 45° 120° is the exterior angle of the triangle. By the Triangle Exterior Angle Conjecture, 120° = 90° + a 120° – 90° = a 30° = a 120° OR, 120° and b are supplementary So, b= 180° - 120° b= 60° And, a = 180 – (90 +b) = 180 – (90-60) a = 30° Discovering Geometry Chapter 4 Test Review HGSH

Discovering Geometry Chapter 4 Test Review HGSH 50° By the Triangle Exterior Angle Conjecture x= 50° + 65° x= 115° 65° Another way, by the Triangle Sum Conjecture, the sum of the interior angles of a triangle equals 180°. So the third angle is: 180° – ( 65° +50°) = 65° and x + 65° = 180° since they are supplementary x= 180° – 65° x= 115° Discovering Geometry Chapter 4 Test Review HGSH

Discovering Geometry Chapter 4 Test Review HGSH By the Triangle Inequality Conjecture, the sum of two of the legs has to be greater than the third. 22cm + 29cm = 51cm and it’s not greater than 52cm. One of the two, 22cm or 29cm legs need to increase so that the sum of the two is greater than 52 cm 52 22 29 Side-Angle Inequality Conjecture 180° – ( 65° + 55°) = 60° 60° From least to greatest: j, k, l 55° 65° Discovering Geometry Chapter 4 Test Review HGSH

Discovering Geometry Chapter 4 Test Review HGSH 11 cm z A B C D E F 13° 25° Remember that CPCTC A  D 180° = A + 25° + 13° 180° – 38° = A 142° = A (CAB) so, by CPCTC 142° = D By CPCTC, AB  DE BC  EF AC  DF Discovering Geometry Chapter 4 Test Review HGSH

Discovering Geometry Chapter 4 Test Review HGSH 55° 45° 88° 180° 110° By the Triangle Exterior Angle Conjecture x + x= 110° 2x= 110° x=55° B C D E T U V W Discovering Geometry Chapter 4 Test Review HGSH

Discovering Geometry Chapter 4 Test Review HGSH AD  CD  ADB   CDB and BD is common to both triangles. Therefore we have SAS. Discovering Geometry Chapter 4 Test Review HGSH

Discovering Geometry Chapter 4 Test Review HGSH 4 cm, 15 cm, 20 cm 12 cm, 11 cm, 20 cm 5 cm, 5 cm, 10 cm 14 cm, 5 cm, 20 cm x=79°; y=101° x=22°; y=101° x=79°; y=68° x=22°; y=79° 101° Because the Triangle is an Isosceles Triangle, the base angles are equal. So, then y = 180° – 101° (Supplementary Angles) y=79° Therefore, 2y+x= 180° 2(79°) + x = 180° x = 180° – 158° = 22° Discovering Geometry Chapter 4 Test Review HGSH

Discovering Geometry Chapter 4 Test Review HGSH

Discovering Geometry Chapter 4 Test Review HGSH

Discovering Geometry Chapter 4 Test Review HGSH By the Isosceles Triangle Conjecture, the base angles of this Isosceles triangle are equal. So 2x + 100° = 180° 2x = 80° x=40° 100° 28 By the Converse of the Isosceles Triangle Conjecture, The Triangle is an Isosceles Triangle so the legs that include vertex P are equal, therefore, PQ is 28 mm. Discovering Geometry Chapter 4 Test Review HGSH

Discovering Geometry Chapter 4 Test Review HGSH 20 ft. By the Converse of the Isosceles Triangle Conjecture The Triangle is an Isosceles Triangle so the legs that include vertex G are equal, therefore, The perimeter = 20 + 6 + 6 = 32 ft. mC = 180- (62+58) = 60 Segment BC 62° 58° Discovering Geometry Chapter 4 Test Review HGSH

Discovering Geometry Chapter 4 Test Review HGSH Segment BD, the Angle Bisector of Isosceles Triangle ABC, is also the perpendicular bisector of segment AC making point D the midpoint. Since segment BD starts at vertex B and goes through midpoint D, then by definition, segment BD it is the median of triangle ABC. Discovering Geometry Chapter 4 Test Review HGSH

Discovering Geometry Chapter 4 Test Review HGSH By the Converse of the Isosceles Triangle Conjecture, the Triangle is an Isosceles, but since the base angles are 60°, then by the Triangle Sum Conjecture, 60 + 60 + x = 180, So x = 60, therefore making the triangle an equiangular, equilateral triangle. Therefore, 3y = 33 yards. y = 11 yds. 15 in 16 in 17 in Discovering Geometry Chapter 4 Test Review HGSH

Discovering Geometry Chapter 4 Test Review HGSH

Discovering Geometry Chapter 4 Test Review HGSH

Discovering Geometry Chapter 4 Test Review HGSH