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5.2: Bisectors in Triangles

The triangular face of the Rock and Roll Hall of Fame in Cleveland, Ohio, is isosceles. The length of the base is 229ft. 6 in. What is the length of the highlighted line that lies at the halfway point of both legs of the triangle?. 5.2: Bisectors in Triangles.

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5.2: Bisectors in Triangles

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  1. The triangular face of the Rock and Roll Hall of Fame in Cleveland, Ohio, is isosceles. The length of the base is 229ft. 6 in. What is the length of the highlighted line that lies at the halfway point of both legs of the triangle?

  2. 5.2: Bisectors in Triangles LEQ: How do we use bisector theorems to find lengths in triangles?

  3. Bisectors in Triangles • Perpendicular Bisector Theorem • If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. • Angle Bisector Theorem • IF a point is on the bisector of an angle, then the point is equidistant from the sides of the angle.

  4. Example According to the diagram, how far is K from EH? From ED? What can you conclude about EK? Find the value of x. Find m<DEH. D (2x)˚ E K 10 (x + 20)˚ H

  5. Solve for x: T Y 2x Z 3x-5 W

  6. Work with a partner to answer the questions:CD is the perpendicular bisector of ST and XD. Justify your answers. C • CT= • 12, SAS, CPCTC, p.b.t. • SX= • 4, segment ad. • MT= • 5, P.B.T.,defn.bisect • DY= • 7, P.B.T., defn.bisect • TY= • 4,segment ad. • CX= • 16 SAS, CPCTC, p.b.t. • ST= • 10, seg. Ad. • XY= • 14, seg. Ad. 12 16 S T 5 M X 7 Y D

  7. Pg. 267-269 • 1-4,6-11,27-30,45-48 • Choose: 40 and 43 OR 41 and 44

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