Right+Angles+Congruence+Theorem+(p7)

Created By: Regan Stiles, Dana Bailey, & Grace Doran Hour: 7 ** Ch.2 Right Angles Congruence Theorem **

Right Angle Congruence Theorem Proof:

Definition: Two triangles are congruent if there exists a one-to-one correspondence between their vertices so that the corresponding sides and corresponding angles are congruent. Meaning: All right angles are congruent.

Problems:

1. Given: 1 and 2 are right angles.

**Answers**:


 * ~ __Statements/Conclusion__ ||~ __Justification__ ||
 * 1) [[image:http://library.thinkquest.org/2647/media/symbols/angle.gif width="15" height="15" align="bottom" caption="angle"]]1 and [[image:http://library.thinkquest.org/2647/media/symbols/angle.gif width="15" height="15" align="bottom" caption="angle"]]2 are right angles. || 1) Given ||
 * 2) m[[image:http://library.thinkquest.org/2647/media/symbols/angle.gif width="15" height="15" align="bottom" caption="angle"]]1 = 90 degrees, m[[image:http://library.thinkquest.org/2647/media/symbols/angle.gif width="15" height="15" align="bottom" caption="angle"]]2 = 90 degrees. || 2) [|Definition of right angles] ||
 * 3) m[[image:http://library.thinkquest.org/2647/media/symbols/angle.gif width="15" height="15" align="bottom" caption="angle"]]1 = m[[image:http://library.thinkquest.org/2647/media/symbols/angle.gif width="15" height="15" align="bottom" caption="angle"]]2 || 3) [|Transitive Property] or [|Substitution Property] ||
 * 4) [[image:http://library.thinkquest.org/2647/media/symbols/angle.gif width="15" height="15" align="bottom" caption="angle"]]1 [[image:http://library.thinkquest.org/2647/media/symbols/congruen.gif align="bottom" caption="is congruent to"]] [[image:http://library.thinkquest.org/2647/media/symbols/angle.gif width="15" height="15" align="bottom" caption="angle"]]2 || 4) Angle Congruence Theorem ||

Theorem of Right Angle Congurence.
**Theorem**: If 2∠’s of Δ are, the sides opposite those ∠ ’s areiven: Δ ABC ∠A ∠B **Prove:** AC=BC A X B=B X C  1. Draw ∠ bisector CX Construction 2. ∠ 1 ∠ 2 Definition of ∠ bisector 3. ∠ A ∠ B Given 4. CX CX Reflexive Prop 5. ΔCAX ΔCBX AAS property 6. AC BC cpctc property ||
 * **Statement** **Reason**

quick review:

1. What is the degrees of a right angle?

A. 90 degrees B. 180 degrees C. 45 degrees

Answer: A; right angles are 90 degrees