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Section 4.3-A Right Angle Theorem

Section 4.3-A Right Angle Theorem. By Scott Salmon and J.C. Show. Theorem # 23. If two angles are both supplementary and congruent, then they are right angles. WHAT????.

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Section 4.3-A Right Angle Theorem

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  1. Section 4.3-A Right Angle Theorem By Scott Salmon and J.C. Show

  2. Theorem # 23 • If two angles are both supplementary and congruent, then they are right angles.

  3. WHAT???? • Since angle 1 and angle 2 form a straight angle, they are supplementary. Therefore, angle 1 plus angle 2 equals 180 degrees.

  4. Sample Problem#1 C Given: CA congruent CB AQ congruent QB Prove: angle AQC and angle BQC are right angles B A Q

  5. Answer Statements Reasons 1: Given 2: Given 3: If 2 adj. angles form a straight angle( Assumed from diagram), then the angles are suppl. 4: If 2 angles are both suppl. and congruent, then they are right angles 1: CA congruent CB 2: AQ congruent QB 3: Angle AQC is suppl. to angle BQC 4: Angles AQC and BQC are right angles

  6. Sample Problem #2 Z W Given: Triangles SZT and AZT are congruent Prove: Angles STZ and ATZ are right angles S T Q A

  7. Answer Reasons Statements 1: Triangles SZT and AZT are congruent 2: Angle STZ is congruent to angle AZT 3:Angle STZ is suppl. to angle AZT 4:Angle STZ and Angle AZT are right angles 1: Given 2: CPCTC 3: IF two adj. angles form a straight angle, then they are suppl. 4: If two angles are both suppl. and congruent, then they are right angles

  8. Practice Problem #1 D Given: Angle ADB is compl. to BDC and Angle ABDis congruent to angle DBC Find : Measures of ALL angles 65 A C B

  9. Answer Explanation: Angle ADB is 35 degrees (subtraction), ABD is suppl. To CBD (Assumed from diagram) Therefore, angles ABD and CBD are right angles (theorem 23), Angle BCD is 35 degrees (subtraction) and angle BAD is 65 degrees (subtraction) D 65 (35) (65) (90) (90) (35) A B C

  10. Practice Problem #2 Given: Angle TPY is congruent to Angle OPY, Angle TPY is suppl. To angle OPY Prove: TYOR is a rhombus T Y P R O

  11. Answer Reasons Statements 1: Angle TPY is congruent to Angle OPY 2: Angle TPY is suppl. to Angle OPY 3. Angle TPY and OPY are right angles 4: Angle RPT is congruent to OPY, and Angle RPO is congruent to Angle YPT 5:TYOR is a rhombus 1: Given 2: Given 3: Theorem 23 (a right angle theorem) 4: Vertical angles are congruent 5: If a quad’s diagonals are perpendicular, then the quad is a rhombus

  12. Works Cited • Rhoad, Richard, George Milauskas, and Robert Whipple. Geometry for Enjoyment and Challenge. Evanston, IL: McDougal, Littell, 1991. Print.

  13. Math Rap

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