holt geometry proving constructions valid ch. 6 proving constructions valid holt geometry lesson...
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Holt Geometry
Proving Constructions ValidCh. 6 Proving Constructions Valid
Holt Geometry
Lesson PresentationLesson 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, 45. ∆ADC ∆ADB
6. CPCTE6. 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,BAC AD and as constructed11111111111111
1.
7. 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.
,AB CD and as constructed
Holt Geometry
Proving Constructions Valid
Example 1 Continued
5. SSS Steps 3, 45. ∆ADC ∆BDC
6. CPCTE6. ACD BCD
7. Reflex. Prop. of
8. SAS Steps 2, 5, 68. ∆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,AB CD and as constructed1.
Holt Geometry
Proving Constructions Valid
13. Def. of bisector
12. CPCTE
11. 2 ’s in linear pr = ―> sides
14. CD is the perpendicular bisector of AB.
Statements Reasons
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