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Are YOU ready? Amara Majeed

CHAPTER TEST REVIEW. Are YOU ready? Amara Majeed. Fill in the blanks. The _____________ Angles Theorem states that if 2 angles of one triangle are ___________ to 2 angles of another triangle, then the __________ pair of angles are also ___________.

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Are YOU ready? Amara Majeed

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  1. CHAPTER TEST REVIEW Are YOU ready? Amara Majeed

  2. Fill in the blanks. The _____________ Angles Theorem states that if 2 angles of one triangle are ___________ to 2 angles of another triangle, then the __________ pair of angles are also ___________

  3. The THIRD Angles Theorem states that if 2 angles of one triangle are CONGRUENT to 2 angles of another triangle, then the THIRD pair of angles are also CONGRUENT.

  4. Match these Postulates. SAS Postulate SSS Postulate ASA Postulate a. If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle, then the triangles are congruent. b. If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. c. If 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent.

  5. SAS Postulate SSS Postulate ASA Postulate a. If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle, then the triangles are congruent. b. If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. c. If 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent.

  6. Find the measure of Angle B. B 2x+3 . 5x-60 15° A C D

  7. The sum of the remote interior angles = the exterior angle. 2x+3+15 <-----Sum of Remote interior angles 2x+18 = 5x-60 <------Set the sum of the remote interior angles equal to the exterior angle. 18 = 3x-60 <-------Subtract 2x. 78 = 3x <--------Add 60. x= 26<-------Divide by 3. 2(26) + 3 = 55

  8. S R Given: RS if perpendicular to ST. TU is perpendicular to ST. V is the midpoint of ST.Prove: ∆RSV is congruent to ∆UTV. V T U STATEMENT 1) RS is perpendicular to ST, TU is perpendicular to ST, V is the midpoint of ST. 2) SV is congruent to TV. 3) Angle UVT is congruent to Angle RVS. 4) RS is parallel to UT. 5) Angle S is congruent to Angle T. 6) ∆RSV is congruent to ∆UTV. Reason Given Def. Of midpoint Vertical Angles Theorem ______?_______ ______?_______ ______?_______

  9. Fill in the blanks. ______________Parts of ______________ triangles are ______________. AAS Theorem: If 2 angles and a ____________ side of 1 triangle are congruent to 2 __________ and a ____________ side of another triangle, then the triangles are ____________. HL Theorem: If the ___________ and a ___________ of one ___________ triangle are congruent to the ____________ and __________ of another ___________ triangle, then the triangles are congruent.

  10. CORRESPONDING Parts of CONGRUENT triangles are CONGRUENT. AAS Theorem: If 2 angles and a NON-INCLUDED side of 1 triangle are congruent to 2 ANGLES and a NON-INCLUDED side of another triangle, then the triangles are CONGRUENT. HL Theorem: If the HYPOTENUSE and a LEG of one RIGHT triangle are congruent to the HYPOTENUSE and a LEG of another RIGHT triangle, then the triangles are congruent.

  11. S R Given: RS if perpendicular to ST. TU is perpendicular to ST. V is the midpoint of ST.Prove: ∆RSV is congruent to ∆UTV. V T U PROVE Given Def. Of midpoint Vertical Angles theorem If 2 lines are perpendicular to the same line, then they are parallel Alternate Interior Angles Theorem ASA Postulate STATEMENT 1) RS is perpendicular to ST, TU is perpendicular to ST, V is the midpoint of ST. 2) SV is congruent to TV. 3) Angle UVT is congruent to Angle RVS. 4) RS is parallel to UT. 5) Angle S is congruent to Angle T. 6) ∆RSV is congruent to ∆UTV.

  12. Given: FG is congruent to OG, GR bisects FO.Prove: Angle F is congruent to Angle O. G F O R STATEMENT FG is congruent to OG, GR bisects FO. GR is congruent to GR. _____?______ ∆GFR is congruent to ∆GOR. Angle F is congruent to Angle O. REASON Given ____?_____ Def. Of Segment Bisector ___?____ ___?____

  13. STATEMENT FG is congruent to OG, GR bisects FO. GR is congruent to GR. FR is congruent to RO. ∆GFR is congruent to ∆GOR. Angle F is congruent to Angle O. REASON Given Reflexive POC Def. Of Segment Bisector SSS Postulate CPCTC

  14. Which theorem or postulate can be used to prove these two triangles congruent?

  15. HL THEOREM This line segment is congruent to itself. It is a leg of both triangles, since it makes a right angle with the other leg. Therefore, since the hypotenuse and leg of one triangle is congruent to the hypotenuse and leg of the other triangle, according to the HL theorem, the two triangles are congruent. This is a right triangle. Therefore, since it is supplementary to this angle, both triangles are classified as right triangles.

  16. BONUS ROUND! Name the 2 simple corollaries present in this unit. ($500 each) NAME THIS POSTULATE: The sum of the lengths of any 2 sides of a triangle is greater than the length of the third side. ($500)

  17. Corollaries:The acute angles of a right triangle are complementary. The measure of each angle of an equiangular triangle is 60°.This is the TRIANGLE INEQUALITY POSTULATE.

  18. T Given: E is the midpoint of MJ. TE is perpendicular to MJ. Prove: ∆MET is congruent to ∆JET. M J E STATEMENT E is the midpoint of MJ, TE is perpendicular to MJ. TE is congruent to TE. ME is congruent to EJ. Angle TEM=90°, Angle TEJ=90° Angle TEM is congruent to Angle TEJ. ∆MET is congruent to ∆JET. REASON Given Reflexive POC ____________ ____________ ____________ ____________

  19. STATEMENT E is the midpoint of MJ, TE is perpendicular to MJ. TE is congruent to TE. ME is congruent to EJ. Angle TEM=90°, Angle TEJ=90° Angle TEM is congruent to Angle TEJ. ∆MET is congruent to ∆JET. REASON Given Reflexive POC Def. of midpoint Def. Of perpendicular lines Transitive POC SAS postulate

  20. P Given: Isosceles ∆PQR, base QR, PA is congruent to PBProve: AR is congruent to BQ A B R Q REASON Given Reflexive POC _________________ _________________ _________________ STATEMENT Isosceles ∆PQR, base QR, PA is congruent to PB Angle P is congruent to Angle P PQ is congruent to PR ∆QPB is congruent to ∆RPA AR is congruent to BQ

  21. STATEMENT Isosceles ∆PQR, base QR, PA is congruent to PB Angle P is congruent to Angle P PQ is congruent to PR ∆QPB is congruent to ∆RPA AR is congruent to BQ REASON Given 2) Reflexive POC 3) Def. Of Isosceles ∆ 4) SAS postulate 5) CPCTC

  22. Can a triangle have the following measures? 1) 2, 4, 4 8, 8, 8 3) 3, 1, 1 4) 5, 6, 7

  23. YES YES NO YES

  24. Any questions answered incorrectly will cost DOUBLE the amount of points. (Each question is 200 points.) State which postulate or theorem, if any, proves that the two triangles are congruent. 1) 2)

  25. 1) NONE2) AAS THEOREM

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