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# TechMathI - 4.4 - Isosceles and Right Triangle Theorems

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### TechMathI - 4.4 - Isosceles and Right Triangle Theorems

1. 1. Bell Ringer <ul><li>Let’s review the homework! </li></ul>
2. 2. Isosceles Triangles
3. 3. Definitions <ul><li>The two angles in an isosceles triangle adjacent to the base of the triangle are called base angles . </li></ul><ul><li>The angle opposite the base is called the vertex angle . </li></ul>Base Angle Base Angle Vertex Angle
4. 4. Definitions - Review ABC is an isosceles triangle. Name each item(s): Vertex Angle Base Legs Base Angles AC AB, CB Side opposite C AB Angle opposite BC
5. 5. A C B A B C A C B Yes Yes No
6. 6. Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
7. 7. Example 1 Find the measure of each angle. x + x + 30 o = 180 o 2x + 30 o = 180 o 2x = 150 o x = 75 o
8. 8. Example 2 Find the length of each side. 3x – 6 2x 6 3x – 6 = 6 3x = 12 x = 4 EF = 6 EG = 8
9. 9. Example 3 Find the measure of each angle. (2x – 4) + (x + 2) + (x + 2) = 180 o 4x = 180 o x = 45 o
10. 10. Hypotenuse-Leg (HL) Congruence Theorem <ul><li>If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent. </li></ul>A B C D E F
11. 11. Practice - What do we still need to know to prove the triangles are congruent? C A B M N F P
12. 12. Practice <ul><li>Find the measure of the missing angles and tell which theorems you used. </li></ul>50° A B C A B C
13. 13. You try! <ul><li>Is there enough information to prove the triangles are congruent? </li></ul>S R T U V W Yes No No
14. 14. 2x 2x x 62