Chapter 5: Relationships in Triangles

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Presentation transcript:

Chapter 5: Relationships in Triangles New Homework Calendar Chapter 5 test: December 19th

5-1 bisectors of Triangles

Perpendicular Bisectors

Example Find BC. Answer: 8.5

Example Find XY. Answer: 6

Example Find PQ. Who wants to explain it? Answer: 7

TOO Find NO. A. 4.6 B. 9.2 C. 18.4 D. 36.8

TOO Find TU. A. 2 B. 4 C. 8 D. 16

TWAP Find EH. A. 8 B. 12 C. 16 D. 20

Circumcenter Theorem

Example (just watch.. Don’t write) GARDEN A triangular-shaped garden is shown. Can a fountain be placed at the circumcenter and still be inside the garden? By the Circumcenter Theorem, a point equidistant from three points is found by using the perpendicular bisectors of the triangle formed by those points.

Example (continued) Copy ΔXYZ, and use a ruler and protractor to draw the perpendicular bisectors. The location for the fountain is C, the circumcenter of ΔXYZ, which lies in the exterior of the triangle. C Answer: No, the circumcenter of an obtuse triangle is in the exterior of the triangle.

Think-Pair-Share BILLIARDS A triangle used to rack pool balls is shown. Would the circumcenter be found inside the triangle? A. No, the circumcenter of an acute triangle is found in the exterior of the triangle. B. Yes, circumcenter of an acute triangle is found in the interior of the triangle.

Angle Bisectors

Example A. Find DB. Answer: DB = 5

Example Find m WYZ. Answer: m<WYZ = 28

Example Find QS. Answer: So, QS = 4(3) – 1 = 11.

TOO Find the measure of SR. A. 22 B. 5.5 C. 11 D. 2.25

Incenter Theorem

Example Find ST if S is the incenter of ΔMNP. Find ST by using the Pythagorean Theorem. a2 + b2 = c2 Pythagorean Theorem 82 + SU2 = 102 64 + SU2 = 100

Example 4 SU2 = 36 SU = 6 Take the square root of each side. Since ST = SU, ST = 6. Answer: ST = 6

TWAP (Hint: Use Pyth. Thm) A. Find the measure of GF if D is the incenter of ΔACF. A. 12 B. 144 C. 8 D. 65 Find <C <F=58 <A=70 <C=52

Homework Pg. 329 #9 - 14, 17-30, 32-35, 48, 54