5 4 Isosceles and Equilateral Triangles Geometry What
![5. 4 Isosceles and Equilateral Triangles Geometry What conjectures can you make about congruent 5. 4 Isosceles and Equilateral Triangles Geometry What conjectures can you make about congruent](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-1.jpg)
![Topic/Objective Use properties of isosceles triangles. n Use properties of equilateral triangles. n 30 Topic/Objective Use properties of isosceles triangles. n Use properties of equilateral triangles. n 30](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-2.jpg)
![Opposite Angles and Sides E EF is opposite D. E is opposite side DF. Opposite Angles and Sides E EF is opposite D. E is opposite side DF.](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-3.jpg)
![Isosceles Triangles Vertex Angle Leg Base Angles Base 30 November 2020 Geometry 5. 4 Isosceles Triangles Vertex Angle Leg Base Angles Base 30 November 2020 Geometry 5. 4](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-4.jpg)
![A construction. Begin with an isosceles triangle, ABC. C Draw the angle bisector from A construction. Begin with an isosceles triangle, ABC. C Draw the angle bisector from](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-5.jpg)
![Theorem 5. 6 Base Angles Theorem. If two sides of a triangle are congruent, Theorem 5. 6 Base Angles Theorem. If two sides of a triangle are congruent,](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-6.jpg)
![Visually: This: Means this: The base angles of an isosceles triangle are congruent. 30 Visually: This: Means this: The base angles of an isosceles triangle are congruent. 30](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-7.jpg)
![Example Problem Solve for x. x + 52 = 180 52° 2 x + Example Problem Solve for x. x + 52 = 180 52° 2 x +](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-8.jpg)
![Example 2 Solve for x and y. 42° x° y° In an isosceles triangle, Example 2 Solve for x and y. 42° x° y° In an isosceles triangle,](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-9.jpg)
![Example 3. You try it. Find x and y. y° y = 32. 5° Example 3. You try it. Find x and y. y° y = 32. 5°](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-10.jpg)
![Example 4 Solve for x. (2 x)° 3 x – 25 = 2 x Example 4 Solve for x. (2 x)° 3 x – 25 = 2 x](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-11.jpg)
![Theorem 5. 7 Converse of the Base Angles Theorem. n If two angles of Theorem 5. 7 Converse of the Base Angles Theorem. n If two angles of](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-12.jpg)
![Example 5 4 x + 52 4(8) + 52 = 84 Solve for x, Example 5 4 x + 52 4(8) + 52 = 84 Solve for x,](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-13.jpg)
![Example 6 You do it. Find the length of each side. 40 4 x Example 6 You do it. Find the length of each side. 40 4 x](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-14.jpg)
![Equilateral Triangles Corollaries to Base Angles Theorem If a triangle is equilateral, then it Equilateral Triangles Corollaries to Base Angles Theorem If a triangle is equilateral, then it](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-15.jpg)
![30 November 2020 Geometry 5. 4 Isosceles, Equilateral Triangles 16 30 November 2020 Geometry 5. 4 Isosceles, Equilateral Triangles 16](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-16.jpg)
![Example 7 All sides are congruent. Solve for x. 3 x – 10 = Example 7 All sides are congruent. Solve for x. 3 x – 10 =](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-17.jpg)
![One last problem. Solve for x and y. y° x° 50° Solution… 30 November One last problem. Solve for x and y. y° x° 50° Solution… 30 November](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-18.jpg)
![Solution… 80° y° 50° ? 40° x° 50° 70° 60° This triangle is equilateral. Solution… 80° y° 50° ? 40° x° 50° 70° 60° This triangle is equilateral.](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-19.jpg)
![Summarize what you have learned today n The base angles of an isosceles triangle Summarize what you have learned today n The base angles of an isosceles triangle](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-20.jpg)
- Slides: 20
![5 4 Isosceles and Equilateral Triangles Geometry What conjectures can you make about congruent 5. 4 Isosceles and Equilateral Triangles Geometry What conjectures can you make about congruent](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-1.jpg)
5. 4 Isosceles and Equilateral Triangles Geometry What conjectures can you make about congruent angles and sides?
![TopicObjective Use properties of isosceles triangles n Use properties of equilateral triangles n 30 Topic/Objective Use properties of isosceles triangles. n Use properties of equilateral triangles. n 30](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-2.jpg)
Topic/Objective Use properties of isosceles triangles. n Use properties of equilateral triangles. n 30 November 2020 Geometry 5. 4 Isosceles, Equilateral Triangles 2
![Opposite Angles and Sides E EF is opposite D E is opposite side DF Opposite Angles and Sides E EF is opposite D. E is opposite side DF.](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-3.jpg)
Opposite Angles and Sides E EF is opposite D. E is opposite side DF. D 30 November 2020 F Geometry 5. 4 Isosceles, Equilateral Triangles 3
![Isosceles Triangles Vertex Angle Leg Base Angles Base 30 November 2020 Geometry 5 4 Isosceles Triangles Vertex Angle Leg Base Angles Base 30 November 2020 Geometry 5. 4](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-4.jpg)
Isosceles Triangles Vertex Angle Leg Base Angles Base 30 November 2020 Geometry 5. 4 Isosceles, Equilateral Triangles 4
![A construction Begin with an isosceles triangle ABC C Draw the angle bisector from A construction. Begin with an isosceles triangle, ABC. C Draw the angle bisector from](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-5.jpg)
A construction. Begin with an isosceles triangle, ABC. C Draw the angle bisector from the vertex angle. The angle bisector intersects the base at M. ACM BCM. Why? A M B SAS A B. Why? CPCTC 30 November 2020 Geometry 5. 4 Isosceles, Equilateral Triangles 5
![Theorem 5 6 Base Angles Theorem If two sides of a triangle are congruent Theorem 5. 6 Base Angles Theorem. If two sides of a triangle are congruent,](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-6.jpg)
Theorem 5. 6 Base Angles Theorem. If two sides of a triangle are congruent, then the angles opposite them are congruent. n (Easy form) The base angles of an isosceles triangle are congruent. n 30 November 2020 Geometry 5. 4 Isosceles, Equilateral Triangles 6
![Visually This Means this The base angles of an isosceles triangle are congruent 30 Visually: This: Means this: The base angles of an isosceles triangle are congruent. 30](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-7.jpg)
Visually: This: Means this: The base angles of an isosceles triangle are congruent. 30 November 2020 Geometry 5. 4 Isosceles, Equilateral Triangles 7
![Example Problem Solve for x x 52 180 52 2 x Example Problem Solve for x. x + 52 = 180 52° 2 x +](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-8.jpg)
Example Problem Solve for x. x + 52 = 180 52° 2 x + 52 = 180 2 x = 128 x° 30 November 2020 x° x = 64 Geometry 5. 4 Isosceles, Equilateral Triangles 8
![Example 2 Solve for x and y 42 x y In an isosceles triangle Example 2 Solve for x and y. 42° x° y° In an isosceles triangle,](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-9.jpg)
Example 2 Solve for x and y. 42° x° y° In an isosceles triangle, base angles are congruent. So y is… 42° Now use the triangle sum theorem: x + 42 = 180 x + 84 = 180 x = 96° 30 November 2020 Geometry 5. 4 Isosceles, Equilateral Triangles 9
![Example 3 You try it Find x and y y y 32 5 Example 3. You try it. Find x and y. y° y = 32. 5°](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-10.jpg)
Example 3. You try it. Find x and y. y° y = 32. 5° x° 2 y + 115 = 180 2 y = 65 x = 65° 50° y° 50° 32. 5°` y° 115° 65° x° 2 x + 50 = 180 – 65 = 115 2 x = 130 x = 65 30 November 2020 Geometry 5. 4 Isosceles, Equilateral Triangles 10
![Example 4 Solve for x 2 x 3 x 25 2 x Example 4 Solve for x. (2 x)° 3 x – 25 = 2 x](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-11.jpg)
Example 4 Solve for x. (2 x)° 3 x – 25 = 2 x x = 25 (3 x – 25)° 30 November 2020 Geometry 5. 4 Isosceles, Equilateral Triangles 11
![Theorem 5 7 Converse of the Base Angles Theorem n If two angles of Theorem 5. 7 Converse of the Base Angles Theorem. n If two angles of](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-12.jpg)
Theorem 5. 7 Converse of the Base Angles Theorem. n If two angles of a triangle are congruent, then the sides opposite them are congruent. n 30 November 2020 Geometry 5. 4 Isosceles, Equilateral Triangles 12
![Example 5 4 x 52 48 52 84 Solve for x Example 5 4 x + 52 4(8) + 52 = 84 Solve for x,](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-13.jpg)
Example 5 4 x + 52 4(8) + 52 = 84 Solve for x, then find the length of the legs. 2 x + 68 Since base angles are equal, opposite sides are equal. 4 x + 52 = 2 x + 68 2 x + 52 = 68 2 x = 16 x=8 30 November 2020 Geometry 5. 4 Isosceles, Equilateral Triangles 13
![Example 6 You do it Find the length of each side 40 4 x Example 6 You do it. Find the length of each side. 40 4 x](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-14.jpg)
Example 6 You do it. Find the length of each side. 40 4 x – 2 5 x 30 5 x = 3 x + 16 2 x = 16 x=8 3 x + 16 40 30 November 2020 Geometry 5. 4 Isosceles, Equilateral Triangles 14
![Equilateral Triangles Corollaries to Base Angles Theorem If a triangle is equilateral then it Equilateral Triangles Corollaries to Base Angles Theorem If a triangle is equilateral, then it](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-15.jpg)
Equilateral Triangles Corollaries to Base Angles Theorem If a triangle is equilateral, then it is also equiangular. n If a triangle is equiangular, then it is also equilateral. n 30 November 2020 Geometry 5. 4 Isosceles, Equilateral Triangles 15
![30 November 2020 Geometry 5 4 Isosceles Equilateral Triangles 16 30 November 2020 Geometry 5. 4 Isosceles, Equilateral Triangles 16](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-16.jpg)
30 November 2020 Geometry 5. 4 Isosceles, Equilateral Triangles 16
![Example 7 All sides are congruent Solve for x 3 x 10 Example 7 All sides are congruent. Solve for x. 3 x – 10 =](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-17.jpg)
Example 7 All sides are congruent. Solve for x. 3 x – 10 = x + 10 2 x = 20 3 x – 10 x + 10 x = 10 2 x = x + 10 x = 10 2 x 3 x – 10 = 2 x x – 10 = 0 x = 10 30 November 2020 Geometry 5. 4 Isosceles, Equilateral Triangles 17
![One last problem Solve for x and y y x 50 Solution 30 November One last problem. Solve for x and y. y° x° 50° Solution… 30 November](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-18.jpg)
One last problem. Solve for x and y. y° x° 50° Solution… 30 November 2020 Geometry 5. 4 Isosceles, Equilateral Triangles 18
![Solution 80 y 50 40 x 50 70 60 This triangle is equilateral Solution… 80° y° 50° ? 40° x° 50° 70° 60° This triangle is equilateral.](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-19.jpg)
Solution… 80° y° 50° ? 40° x° 50° 70° 60° This triangle is equilateral. Each angle is? 60° These angles form straight angle. The missing angle is? 30 November 2020 Geometry 5. 4 Isosceles, Equilateral Triangles 19
![Summarize what you have learned today n The base angles of an isosceles triangle Summarize what you have learned today n The base angles of an isosceles triangle](https://slidetodoc.com/presentation_image_h/c6ad0980ffedd56977d10bbcaa76e4cc/image-20.jpg)
Summarize what you have learned today n The base angles of an isosceles triangle are congruent. n Equilateral triangles are Equiangular. 30 November 2020 Geometry 5. 4 Isosceles, Equilateral Triangles 20
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