CK-12 Geometry Concepts

5.3. Angle Bisectors in Triangles http://www.ck12.org

Is there enough information to determine if

−→

ABis the angle bisector of^6 CAD? Why or why not?

7.

8.

9. Fill in the blanks in the Angle Bisector Theorem Converse.

Given:AD∼=DC, such thatADandDCare the shortest distances to

−→

BAand

−→

BC

Prove:

−→

BDbisects^6 ABC

TABLE5.4:

Statement Reason

1.

2. The shortest distance from a point to a line is perpen-
   dicular.
   3.^6 DABand^6 DCBare right angles
   4.^6 DAB∼=^6 DCB
   5.BD∼=BD


3. 4 ABD∼= 4 CBD


4. CPCTC


5. 
   

−→

BDbisects^6 ABC

Determine if the following descriptions refer to the incenter or circumcenter of the triangle.

10. A lighthouse on a triangular island is equidistant to the three coastlines.


11. A hospital is equidistant to three cities.


12. A circular walking path passes through three historical landmarks.


13. A circular walking path connects three other straight paths.

Multi- Step Problem

14. Draw^6 ABCthroughA( 1 , 3 ),B( 3 ,− 1 )andC( 7 , 1 ).


15. Use slopes to show that^6 ABCis a right angle.


16. Use the distance formula to findABandBC.


17. Construct a line perpendicular toABthroughA.


18. Construct a line perpendicular toBCthroughC.


19. These lines intersect in the interior of^6 ABC. Label this pointDand draw

−→

BD.

20. Is

−→

BDthe angle bisector of^6 ABC? Justify your answer.