5.4 Isosceles and Equilateral Triangles

Slides:



Advertisements
Similar presentations
4-5 Isosceles and Equilateral Triangles Learning Goal 1. To use and apply properties of isosceles and equilateral triangles.
Advertisements

Adapted from Walch Education Isosceles triangles have at least two congruent sides, called legs. The angle created by the intersection of the legs is.
Isosceles Triangles Geometry D – Chapter 4.6. Definitions - Review Define an isosceles triangle. A triangle with two congruent sides. Name the parts of.
4.6 The Isosceles Triangle Theorems Base Angles and Opposite Sides Hypotenuse - Leg.
The Isosceles Triangles Theorems Section 4-6 Isosceles Triangle Theorem  If 2 sides of a triangle are congruent, then the angles opposite those sides.
4.5 - Isosceles and Equilateral Triangles. Isosceles Triangles The congruent sides of an isosceles triangles are called it legs. The third side is the.
Isosceles and Equilateral Triangles Chapter 4 Section 5.
ISOSCELES TRIANGLES 1 Modified by Lisa Palen. PARTS OF AN ISOSCELES TRIANGLE An isosceles triangle is a triangle with at least two congruent sides. The.
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.
Isosceles and Equilateral Triangles Section 5-1. Isosceles Triangle A triangle with at least two congruent sides. Leg Leg Base Vertex Angle Base Angles.
Warm-Up Find the value of x. x x - 3. GEOMETRY 4-8 Isosceles and Equilateral Triangles.
Properties of Special Triangles 4-5 Objective: To use and apply properties of isosceles and equilateral triangles.
1 4-5 Isosceles and Equilateral Triangles State and apply the Isosceles Triangle Theorem and its converse State and apply the corollaries for equilateral.
Use Isosceles and Equilateral Triangles
4-6 Isosceles & Equilateral Triangles
4.5: Isosceles and Equilateral Triangles Objective: To use and apply properties of isosceles and equilateral triangles.
4-5 Isosceles and Equilateral Triangles
1 Isosceles and Equilateral Triangles. 2 Parts of an Isosceles Triangle An isosceles triangle is a triangle with two congruent sides. The congruent sides.
CH. 4.7 USE ISOSCELES & EQUILATERAL TRIANGLES. VOCAB Leg: 2 sides of isosceles triangle Leg Vertex Angle: Angle formed by the two legs Base: 3 rd side.
Geometry Ms. Stawicki.  1) To use and apply properties of isosceles triangles.
Triangles Review.
5.4 – Equilateral and Isosceles Triangles
Section 4-4: The Isosceles Triangle Theorems
Section 4-5: Isosceles and Equilateral Triangles.
Isosceles Triangle ABC Vertex Angle Leg Base Base Angles.
4.6: Isosceles and Equilateral Triangles
Triangle Sum Theorem The sum of the angle measures in a triangle is 180 degrees.
4.3 ISOSCELES AND EQUILATERAL TRIANGLES. VOCABULARY Two angles of an isosceles triangle are always congruent. These are the angles opposite the congruent.
Triangle Congruence 4.5 Isosceles and Equilateral Triangles.
Isosceles Triangles Theorems Theorem 8.12 – If two sides of a triangle are equal in measure, then the angles opposite those sides are equal in measure.
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.
Isosceles Triangles A B C
Use isosceles and equilateral triangles
Isosceles and Equilateral Triangles
4.5 Isosceles and Equilateral Triangles
4-5 Isosceles and Equilateral Triangles
Warm Up [On back counter]
Properties of Isosceles & Equilateral Triangles
The Isosceles Triangle Theorems
4.7 Use Isosceles and Equilateral Triangles
Date: Topic: Isosceles Triangle Theorem (6.1.C)
Warm Up Yes, ASA. Yes, AAS. Not enough info. Yes, SAS.
Isosceles & Equilateral Triangles
Types of Triangles and Their Properties
Section 4.5 isosceles & equilateral triangles
The Isosceles Triangle Theorems
Triangles Review.
Objective: To use and apply properties of isosceles triangles.
Lesson 3-2 Isosceles Triangles.
4.5 - Isosceles and Equilateral Triangles
(The Isosceles Triangle Theorems)
Warm-up Find x a) b).
The Isosceles Triangle Theorems
DRILL Write the converse of the statement:
4.1 Congruent Figures -Congruent Polygons: have corresponding angles and sides -Theorem 4.1: If 2 angles of 1 triangle are congruent to 2 angles of another.
7.2 Isosceles and Equilateral Triangles
Warm-up Find x a) b).
4.7 Use Isosceles and Equilateral Triangles
Isosceles, Equilateral, and Right Triangles
4.6 Isosceles Triangles.
Isosceles and Equilateral Triangles
5.4 Isosceles and Equilateral Triangles.
Isosceles, Equilateral, and Right Triangles
(The Isosceles Triangle Theorems)
4.8 – Use Isosceles and Equilateral Triangles
Equilateral TRIANGLES
Isosceles and Equilateral Triangles
Module 15: Lesson 2 Isosceles & Equilateral Triangles
Section 3.3 Isosceles Triangles
Presentation transcript:

5.4 Isosceles and Equilateral Triangles Geometry What conjectures can you make about congruent angles and sides?

Geometry 5.4 Isosceles, Equilateral Triangles Topic/Objective Use properties of isosceles triangles. Use properties of equilateral triangles. April 25, 2018 Geometry 5.4 Isosceles, Equilateral Triangles

Opposite Angles and Sides EF is opposite D. E is opposite side DF. D F April 25, 2018 Geometry 5.4 Isosceles, Equilateral Triangles

Geometry 5.4 Isosceles, Equilateral Triangles Isosceles Triangles Vertex Angle Leg Leg Base Angles Base April 25, 2018 Geometry 5.4 Isosceles, Equilateral Triangles

Geometry 5.4 Isosceles, Equilateral Triangles A construction. Begin with an isosceles triangle, ABC. Draw the angle bisector from the vertex angle. The angle bisector intersects the base at M. ACM  BCM. Why? SAS A  B. Why? CPCTC C A B M April 25, 2018 Geometry 5.4 Isosceles, Equilateral Triangles

Theorem 5.6 Base Angles Theorem. If two sides of a triangle are congruent, then the angles opposite them are congruent. (Easy form) The base angles of an isosceles triangle are congruent. April 25, 2018 Geometry 5.4 Isosceles, Equilateral Triangles

Geometry 5.4 Isosceles, Equilateral Triangles Visually: This: Means this: The base angles of an isosceles triangle are congruent. April 25, 2018 Geometry 5.4 Isosceles, Equilateral Triangles

Geometry 5.4 Isosceles, Equilateral Triangles Example Problem Solve for x. x + x + 52 = 180 2x + 52 = 180 2x = 128 x = 64 52° x° x° April 25, 2018 Geometry 5.4 Isosceles, Equilateral Triangles

Geometry 5.4 Isosceles, Equilateral Triangles Example 2 Solve for x and y. In an isosceles triangle, base angles are congruent. So y is… 42° Now use the triangle angle sum theorem: x + 42 + 42 = 180 x + 84 = 180 x = 96° 42° x° y° April 25, 2018 Geometry 5.4 Isosceles, Equilateral Triangles

Geometry 5.4 Isosceles, Equilateral Triangles Example 3. You try it. 50° x° y° x = 65° y = 32.5° Find x and y. 50° y° 2y + 115 = 180 2y = 65 y = 32.5° y° 32.5°` 115° x° 65° 65° x° 2x + 50 = 180 2x = 130 x = 65 180 – 65 = 115 April 25, 2018 Geometry 5.4 Isosceles, Equilateral Triangles

Geometry 5.4 Isosceles, Equilateral Triangles Example 4 Solve for x. (2x)° (3x – 25)° 3x – 25 = 2x x = 25 April 25, 2018 Geometry 5.4 Isosceles, Equilateral Triangles

Geometry 5.4 Isosceles, Equilateral Triangles Theorem 5.7 Converse of the Base Angles Theorem. If two angles of a triangle are congruent, then the sides opposite them are congruent. April 25, 2018 Geometry 5.4 Isosceles, Equilateral Triangles

Geometry 5.4 Isosceles, Equilateral Triangles Example 5 Since base angles are equal, opposite sides are equal. 4x + 52 = 2x + 68 2x + 52 = 68 2x = 16 x = 8 4x + 52 2x + 68 4(8) + 52 = 84 Solve for x, then find the length of the legs. April 25, 2018 Geometry 5.4 Isosceles, Equilateral Triangles

Geometry 5.4 Isosceles, Equilateral Triangles Example 6 You do it. Find the length of each side. 5x = 3x + 16 2x = 16 x = 8 40 4x – 2 5x 30 3x + 16 40 April 25, 2018 Geometry 5.4 Isosceles, Equilateral Triangles

Equilateral Triangles Corollaries to Base Angles Theorem If a triangle is equilateral, then it is also equiangular. If a triangle is equiangular, then it is also equilateral. April 25, 2018 Geometry 5.4 Isosceles, Equilateral Triangles

Geometry 5.4 Isosceles, Equilateral Triangles April 25, 2018 Geometry 5.4 Isosceles, Equilateral Triangles

Geometry 5.4 Isosceles, Equilateral Triangles Example 7 Solve for x. All sides are congruent. 3x – 10 = x + 10 2x = 20 x = 10 3x – 10 x + 10 2x 2x = x + 10 x = 10 3x – 10 = 2x x – 10 = 0 x = 10 April 25, 2018 Geometry 5.4 Isosceles, Equilateral Triangles

Geometry 5.4 Isosceles, Equilateral Triangles One last problem. Solve for x and y. x° y° 50° Solution… April 25, 2018 Geometry 5.4 Isosceles, Equilateral Triangles

Geometry 5.4 Isosceles, Equilateral Triangles Solution… This triangle is equilateral. Each angle is? 40° x° 70° 80° y° 60° 70° ? 50° 50° 60° 60° These angles form straight angle. The missing angle is? April 25, 2018 Geometry 5.4 Isosceles, Equilateral Triangles

Geometry 5.4 Isosceles, Equilateral Triangles Summarize what you have learned today The base angles of an isosceles triangle are congruent. Equilateral triangles are Equiangular. April 25, 2018 Geometry 5.4 Isosceles, Equilateral Triangles