Holt Geometry Proving Constructions Valid Ch. 6 Proving Constructions Valid Holt Geometry Lesson Presentation Lesson Presentation

Holt Geometry Proving Constructions Valid Use congruent triangles to prove constructions valid. Objective

Holt Geometry Proving Constructions Valid When performing a compass and straight edge construction, the compass setting remains the same width until you change it. This fact allows you to construct a segment congruent to a given segment. You can assume that two distances constructed with the same compass setting are congruent.

Holt Geometry Proving Constructions Valid The steps in the construction of a figure can be justified by combining: the assumptions of compass and straightedge constructions, and the postulates and theorems that are used for proving triangles congruent.

Holt Geometry Proving Constructions Valid Your figure will be a post-construction drawing, including arcs. You will then have to draw line segments connecting points in your figure so that you can create triangles that appear to be congruent. Drawing line segments will be actual steps in your proof. The reason for introducing a new line segment is the theorem that states “through any two points there is exactly one line.”

Holt Geometry Proving Constructions Valid Given: BAC, and AD by construction Prove: AD is the angle bisector of BAC.

Holt Geometry Proving Constructions Valid Example 1 Continued 5. SSS Steps 3, 4 5. ∆ADC  ∆ADB 6. CPCTE 6. DAC  DAB 7.  angles  angle bisector 4. Reflex. Prop. of  3. Same compass setting used Statements 2. Through any two points there is exactly one line. Reasons 4. AD  AD 3. AC  AB ; CD  BD 2. Draw BD and CD. 1. Given AD is the angle bisector of BAC.

Holt Geometry Proving Constructions Valid Check It Out! Example 1 Given: Prove: CD is the perpendicular bisector of AB.

Holt Geometry Proving Constructions Valid Example 1 Continued 5. SSS Steps 3, 4 5. ∆ADC  ∆BDC 6. CPCTE 6. ACD  BCD 7. Reflex. Prop. of  8. SAS Steps 2, 5, 6 8. ∆ACM  ∆BCM 4. Reflex. Prop. of  3. Same compass setting used Statements 2. Through any two points there is exactly one line. Reasons 7. CM  CM 4. CD  CD 3. AC  BC  AD  BD 2. Draw AC, BC, AD, and BD. 1. Given 1.

Holt Geometry Proving Constructions Valid 13. Def. of bisector 12. CPCTE ’s in linear pr = ―>  sides 14. CD is the perpendicular bisector of AB. StatementsReasons 13. CD bisects AB 12. AM  BM 11. AB  DC Example 1 Continued 10. AMC and BMC are lin. pr. 10. Def. of linear pair 9. AMC  BMC 9. CPCTC 14. Def. of  bisector