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Mastering Triangles: Isosceles, Equilateral, Right Triangles - Properties & Solutions

Learn about isosceles and equilateral triangles, including properties and solution techniques. Also explore right triangles and methods to prove triangle congruence. Solve related problems to enhance your understanding.

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Mastering Triangles: Isosceles, Equilateral, Right Triangles - Properties & Solutions

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  1. Objectives: • Use properties of isosceles and equilateral triangles • Use properties of right triangles

  2. In lesson 4.1, you learned that a triangle is an isosceles if it has at least two congruent sides. The two angles adjacent to the base are the base angles. The angle opposite the base is the vertex angle. Properties of Isosceles Triangles

  3. An EQUILATERAL triangle is a special type of isosceles triangle. Remember:

  4. Find the value of x Find the value of y 3x = 180 X = 60 Equilateral and Isosceles Triangles y° x°

  5. Find the value of x Find the value of y 120° + 2y° = 180° 2y = 60 y = 30 Ex. 2: Using Equilateral and Isosceles Triangles y° x° 60°

  6. Using Properties of Right Triangles • You have learned four ways to prove that triangles are congruent. • Side-Side-Side (SSS) • Side-Angle-Side (SAS) • Angle-Side-Angle (ASA) • Angle-Angle-Side (AAS)

  7. Solve: Solution: Isosceles Triangle X = 180-54-54 X=72

  8. Solve: Solution: Two Isosceles Triangles • 90- 28 = 62 • 180-62-62 = 56 • X=56

  9. Solve: 65 Solution: Two Isosceles Triangles • 180 – 65-65 = 50 • 180 – 50-50 = 80 • X= 80 50 50 =80 50

  10. Solve: Solution: • 120 = 60+60 • 60= 60 vertical angles • X = 60 60 60 60 60 60

  11. Try this one: Solution: 12 = 2x -12 24 = 2x X = 12

  12. One More: Solution: • 180-68-68 = 44 • 90 - 44 = 46 • 4x – 2 = 46 Solve for x 4x = 48 X = 12 44 68

  13. Last One: Solution: • 146 = 13x + 3 • 143 = 13x • 11

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