Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Golden ratio wikipedia , lookup
Euler angles wikipedia , lookup
History of geometry wikipedia , lookup
Reuleaux triangle wikipedia , lookup
Noether's theorem wikipedia , lookup
Riemann–Roch theorem wikipedia , lookup
Rational trigonometry wikipedia , lookup
Brouwer fixed-point theorem wikipedia , lookup
Four color theorem wikipedia , lookup
Trigonometric functions wikipedia , lookup
History of trigonometry wikipedia , lookup
Integer triangle wikipedia , lookup
Geometry Examples: 4.1 – 4.4 Name:____________________________________ Date:___________________ Period:___________ 4.1 In the figure, PQ PS , PR QS . Complete the sentence. P 1. PQ is the ____________________ of the right triangle PQR . 2. In PQR , PQ is the side opposite angle _______________. 3. QS is the ________________ of the isosceles triangle PQS . 4. The legs of PRS are ________ and ________ . 5. ________ is the hypotenuse of PRS . Classify the triangles by (a) its angles and (b) its sides. 6. 7. 8. 40 Q R S 100 9. 60 a)__________ a)__________ a)__________ a)__________ b)___________ b)___________ b)___________ b)___________ Match the triangle description with the most specific name. 10. Side lengths: 2, 3, 4 _____ A. Equilateral 11. Side lengths: 3, 2, 3 _____ B. Scalene 12. Side lengths: 4, 4, 4 _____ C. Obtuse 13. Angle measures: 60, 60, 60 _____ D. Equiangular 14. Angle measures: 30, 60, 90 _____ E. Isosceles 15. Angle measures: 20, 145, 15 _____ F. Right Complete the statement using always, sometimes or never. 16. An isosceles triangle is ________ an equilateral triangle. 17. An obtuse triangle is ________ an isosceles triangle. 18. An interior angle of a triangle and one of its adjacent exterior angles are _______ supplementary. 19. The acute angles of a right triangle are _________ complementary. 20. A triangle ________ has a right angle and an obtuse angle. Find the measure of the numbered angles. 21. 1 40 2 3 95 ________ ________ ________ Find the measure of the exterior angle shown. 22. ________ 2x-8 x 31 4.2 LMN PQR . Find the following. Q 1. m P = ________ N 2. M _______ 3. R _______ 4. m N = ________ 5. PQ = ________ 6. LN ________ 105 L 7. QR ________ 8. List the 6 corresponding 45 congruent parts ________________ ________________ ________________ ________________ R M ________________ 10 cm ________________ 9) Name the four methods you have learned for proving triangles congruent. Only one of these is called a theorem. Why is it called a theorem? _____ _____ _____ _____ _____________________ P Is it possible tp prove that the triangles are congruent? If so, state the postulate or theorem you would use? 10) RST TQR S 11) JKL NML 12) DFE JGH K M F J L T R E N J D H G Q State the third congruence that must be given to prove that ABC DEF using the indicated postulate or theorem. 13) ASA Congruence Postulate 14) AAS Congruence Theorem F A E B D F B A C C D E LOGICAL REASONING: Is it possible to prove that the triangles are congruent? If so, state the postulate or theorem you would use. Also state the congruent triangles. M B 15) R 16) 17) S P S Q T V U T A D C R 18) E F H 19) X K M J 20) W Z G J N L Q Y LOGICAL REASONING: Decide whether enough information is given to prove that the triangles are congruent. If there is enough information, tell which congruence postulate or theorem you would use. 21) ABC , DEC 22) FGH , JKH 23) PQR , SRQ F P B A Q G C H E D K S 24) UVT , WVT 25) R J LMN , TNM 26) YZW , YXW L T T Z W Y X W N M U V 27) ACB , ECD 28) RST , WVU T A GJH , HLK 29) U J G D L B C E W R S H K M V DEVELOPING PROOF: State the third congruence that must be given to prove that PQR STU using the indicated postulate or theorem. (Hint: First sketch PQR and STU . Mark the triangles with the given information.) 30) Given: Q T , PQ ST . Use the AAS Congruence Theorem. 31) Given: R U , PR SU . Use the ASA Congruence Postulate. 32) Given: R U , P S . Use the ASA Congruence Postulate. Use the diagram. Name the included angle between each pair of sides given. K P 34) JK and KL _____ 35) LP and LK _____ 36) KL and JL _____ 37) PK and LK _____ 38) JL and JK _____ 39) KP and PL _____ 40) Use the same diagram to list the 6 corresponding congruent parts. _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ L J 33) Given: PR SU , R U . Use the SAS Congruence Postulate. _____ _____