5-1 Bisectors of Triangles

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Presentation transcript:

5-1 Bisectors of Triangles You used segment and angle bisectors. Identify and use perpendicular bisectors in triangles. Identify and use angle bisectors in triangles.

Perpendicular Bisector Perpendicular bisector is any segment that intersects another segment at its midpoint AND is perpendicular to that segment. K R S J

Perpendicular Bisector A perpendicular bisector of a side of a triangle is a line perpendicular to a side through the midpoint of the side. (Perpendicular and bisects one side only) Perpendicular bisector B C A

Page 324

A. Find BC. BC = AC Perpendicular Bisector Theorem BC = 8.5 Substitution Answer: 8.5

B. Find XY. Answer: 6

C. Find PQ. PQ = RQ Perpendicular Bisector Theorem 3x + 1 = 5x – 3 Substitution 1 = 2x – 3 Subtract 3x from each side. 4 = 2x Add 3 to each side. 2 = x Divide each side by 2. So, PQ = 3(2) + 1 = 7. Answer: 7

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

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

Definitions Concurrent lines – three or more lines intersect at a common point. Point of concurrency – the point where concurrent lines intersect. The point of concurrency is also called the circumcenter of the triangle

Concurrent Lines If three or more coplanar lines intersect at the same point, they are concurrent lines. The point of intersection is the point of concurrency. Concurrent lines Point of concurrency

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Angle Bisector When an angle bisector is used in a triangle, it is a segment. The angle bisector cuts the angle in half and goes to the other side. A B C D Angle bisector

Page 327

A. Find DB. DB = DC Angle Bisector Theorem DB = 5 Substitution Answer: DB = 5

C. Find QS. QS = SR Angle Bisector Theorem 4x – 1 = 3x + 2 Substitution x – 1 = 2 Subtract 3x from each side. x = 3 Add 1 to each side. Answer: So, QS = 4(3) – 1 or 11.

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

B. Find the measure of HFI. C. 15 D. 30

C. Find the measure of UV. A. 7 B. 14 C. 19 D. 25 **Set equal to each other

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A. Find the measure of GF if D is the incenter of ΔACF. B. 144 C. 8 D. 65 **Use Pythagorean Theorem

B. Find the measure of BCD if D is the incenter of ΔACF.

5-1 Assignment Page 329, 2-30 even, skip 4