1 / 12

Lesson Menu

Five-Minute Check (over Lesson 5–5) Then/Now Theorems: Inequalities in Two Triangles Example 1: Use the Hinge Theorem and its Converse Proof: Hinge Theorem Example 2: Real-World Example: Use the Hinge Theorem Example 3: Apply Algebra to the Relationships in Triangles

shona
Télécharger la présentation

Lesson Menu

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. Five-Minute Check (over Lesson 5–5) Then/Now Theorems: Inequalities in Two Triangles Example 1: Use the Hinge Theorem and its Converse Proof: Hinge Theorem Example 2: Real-World Example: Use the Hinge Theorem Example 3: Apply Algebra to the Relationships in Triangles Example 4: Prove Triangle Relationships Using Hinge Theorem Example 5: Prove Relationships Using Converse of Hinge Theorem Lesson Menu

  2. A B Determine whether it is possible to form a triangle with side lengths 5, 7, and 8. A. yes B. no 5-Minute Check 1

  3. A B Determine whether it is possible to form a triangle with side lengths 4.2, 4.2, and 8.4. A. yes B. no 5-Minute Check 2

  4. A B Determine whether it is possible to form a triangle with side lengths 3, 6, and 10. A. yes B. no 5-Minute Check 3

  5. You used inequalities to make comparisons in one triangle. (Lesson 5–3) • Apply the Hinge Theorem or its converse to make comparisons in two triangles. • Prove triangle relationships using the Hinge Theorem or its converse. Then/Now

  6. Concept

  7. In ΔACD and ΔBCD, AC BC, CD  CD, and ACD > BCD. Use the Hinge Theorem and Its Converse A. Compare the measures AD and BD. Answer: By the Hinge Theorem, mACD > mBCD, so AD > DB. Example 1

  8. In ΔABD and ΔBCD, AB CD, BD  BD, and AD > BC. Use the Hinge Theorem and Its Converse B. Compare the measures ABD and BDC. Answer: By the Converse of the Hinge Theorem, ABD > BDC. Example 1

  9. A B C D A. Compare the lengths of FG and GH. A.FG > GH B.FG < GH C.FG  GH D. not enough information Example 1

  10. A B C D B. Compare JKM and KML. A.mJKM > mKML B.mJKM < mKML C.mJKM = mKML D. not enough information Example 1

  11. Use the Hinge Theorem HEALTH Doctors use a straight-leg-raising test to determine the amount of pain felt in a person’s back. The patient lies flat on the examining table, and the doctor raises each leg until the patient experiences pain in the back area. Nitan can tolerate the doctor raising his right leg 35° and his left leg 65° from the table. Which leg can Nitan raise higher above the table? Understand Using the angles given in the problem,you need to determine which leg can be risen higher above the table. Example 2

  12. Use the Hinge Theorem Plan Draw a diagram of the situation. SolveSince Nitan’s legs are the same length and his left leg and the table is the same length in both situations, the Hinge Theorem says his left leg can be risen higher, since 65° > 35°. Example 2

More Related