1 / 18

5-2: Right Triangles

5-2: Right Triangles. Expectation: G2.3.1: Prove that triangles are congruent using SSS, SAS, ASA, AAS and that right triangles are congruent using the hypotenuse leg condition. G2.3.2: Use theorems about congruent triangles to prove additional theorems and solve problems. ACT Prep. l.

yeo-fernandez
Download Presentation

5-2: Right Triangles

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 5-2: Right Triangles • Expectation: • G2.3.1: Prove that triangles are congruent using SSS, SAS, ASA, AAS and that right triangles are congruent using the hypotenuse leg condition. • G2.3.2: Use theorems about congruent triangles to prove additional theorems and solve problems.

  2. ACT Prep l (x+60)° (4x)° m • If line l is parallel to line m below, what is the value of x? • 12 • 15 • 20 • 24 • 30

  3. Leg-Leg Condition What is true about two right triangles that have congruent legs? Why?

  4. Leg-Leg Right Triangle Congruence Theorem (LL) • In 2 right triangles, if the legs of the first are congruent to the legs of the second, then the triangles are congruent.

  5. Hypotenuse Acute Angle Condition C Z A B X Y What is true about the right triangles above? Why?

  6. Hypotenuse Acute Angle Right Triangle Congruence Theorem (HA) • In 2 right triangles, if the hypotenuse and an acute angle of the first are congruent to the hypotenuse and an acute angle of the second, then the triangles are congruent.

  7. C Z A B X Y Leg Acute Angle Condition First case: What is true about the triangles above? Why?

  8. Leg Acute Angle Condition Second case: C Z A B X Y What is true about the triangles above? Why?

  9. Leg Acute Angle Right Triangle Congruence Theorem (LA) • In two right triangles, if a leg and an acute angle of the first are congruent to the corresponding leg and acute angle of the second, then the triangles are congruent.

  10. C Z A B X Y Hypotenuse Leg Condition What is true about the triangles above? Why?

  11. Hypotenuse Leg Right Triangle Congruence Postulate (HL) • In 2 right triangles, if the hypotenuse and a leg of the first are congruent to the hypotenuse and the corresponding leg of the second, then the triangles are congruent.

  12. Can HL be used to conclude the triangles are congruent? Justify.

  13. Can HL be used to conclude the triangles are congruent? Justify.

  14. What additional information would you need to prove the triangles are congruent by HL? B ΔADB ≅ΔCDB D C A

  15. On the real number line, what is the midpoint of -3 and 11? • A. -5 • B. 0 • C. 4 • D. 7 • E. 14

  16. Given: XY ≅ LY, Y is the midpoint of WK and ∠W and ∠K are right angles Prove: XW ≅ LK X L Y K W

  17. Assignment • pages 249 – 250, • 5.1 and 5.2 worksheet

More Related