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Triangle Congruencies

Triangle Congruencies. Lesson 4.4. Opener a) Can you make a triangle using the sides: 5 ft., 12 ft., and 4 ft.? b) One side of a triangle is 12 mm. Another side is 17 mm. What are the possible lengths for the third side?. Q. P. Z. 33°. CNB. 3. Given PQZ. B. c) What is PZ?

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Triangle Congruencies

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  1. Triangle Congruencies Lesson 4.4

  2. Opener a) Can you make a triangle using the sides: 5 ft., 12 ft., and 4 ft.? b) One side of a triangle is 12 mm. Another side is 17 mm. What are the possible lengths for the third side? Q P Z 33° CNB 3 Given PQZ B c) What is PZ? d) What is <Z e) What is < N f) What percent of M&Ms are brown? 62° 10 N C

  3. Isosceles Triangles Conjecture Isosceles Triangle Conjecture If a triangle is isosceles, then base angles are equal. 20° 80° 80°

  4. Exterior Angle Conjecture Exterior Angle Conjecture The measure of an exterior angle of a triangle is equal to the sum of the remote interior angles. 20° 45° 25°

  5. Classwork Review NCA GEA

  6. Classwork Review JAN IEC

  7. Lesson 4.4 - Congruent Triangles Is this a guarantee of triangle congruence? One pair of congruent sides

  8. Notes - Congruent Triangles Is this a guarantee of triangle congruence? One pair of congruent sides NO!

  9. Notes - Congruent Triangles Is this a guarantee of triangle congruence? Two pairs of congruent sides

  10. Notes - Congruent Triangles Is this a guarantee of triangle congruence? Two pairs of congruent sides NO!

  11. Notes - Congruent Triangles Is this a guarantee of triangle congruence? Three pairs of congruent sides

  12. Notes - Congruent Triangles Is this a guarantee of triangle congruence? Three pairs of congruent sides YES! SSS

  13. Notes - Congruent Triangles Is this a guarantee of triangle congruence? Three pairs of congruent angles 25° 65° 90°

  14. Notes - Congruent Triangles Is this a guarantee of triangle congruence? Three pairs of congruent angles 65° 90° 25° NO! 65° 90° 25°

  15. Notes - Congruent Triangles Are these guarantees of triangle congruence? √ SSS AAA SAS SSA ASA SAA

  16. Notes - Congruent Triangles Is this a guarantee of triangle congruence? One pair of congruent angles, two pairs of congruent sides 25° 25° √ SSS AAA SAS SSA ASA SAA

  17. Notes - Congruent Triangles Is this a guarantee of triangle congruence? Two pairs of congruent sides and the included angle √ SSS AAA √ SAS 25° 25° SSA YES! ASA SAS! SAA

  18. Notes - Congruent Triangles Is this a guarantee of triangle congruence? Two pairs of congruent sides and the included angle ABC DEF D A √ SSS E AAA 92° √ SAS 92° SSA B C ASA SAA F An included angle is between the two given sides.

  19. Notes - Congruent Triangles Is this a guarantee of triangle congruence? Two pairs of congruent sides and a non-included angle 65° √ SSS AAA √ SAS SSA ASA SAA

  20. Notes - Congruent Triangles Is this a guarantee of triangle congruence? Two pairs of congruent sides and a non-included angle 65° √ SSS AAA √ SAS SSA ASA SAA

  21. Notes - Congruent Triangles Is this a guarantee of triangle congruence? Two pairs of congruent sides and a non-included angle √ SSS AAA 65° √ SAS SSA ASA SAA

  22. Notes - Congruent Triangles Is this a guarantee of triangle congruence? Two pairs of congruent sides and a non-included angle √ SSS AAA 65° √ SAS SSA ASA SAA

  23. Notes - Congruent Triangles Is this a guarantee of triangle congruence? Two pairs of congruent sides and a non-included angle A ABC DEF B C E √ SSS AAA √ SAS SSA ASA F D SAA NO!

  24. Notes - Congruent Triangles Is this a guarantee of triangle congruence? Two pairs of congruent angles and the included side 25° 90° √ SSS AAA √ SAS SSA ASA SAA

  25. Notes - Congruent Triangles Is this a guarantee of triangle congruence? Two pairs of congruent angles and the included side 25° 90° √ SSS AAA √ SAS SSA ASA YES! SAA ASA!

  26. Notes - Congruent Triangles Is this a guarantee of triangle congruence? Two pairs of congruent angles and the included side ABC B DEF 55° A 65° C E √ SSS AAA √ SAS 65° SSA F 55° √ ASA D SAA ASA!

  27. Notes - Congruent Triangles Is this a guarantee of triangle congruence? Two pairs of congruent angles and the non-included side 35° 90° √ SSS AAA √ SAS SSA √ ASA SAA

  28. Notes - Congruent Triangles Is this a guarantee of triangle congruence? Two pairs of congruent angles and the non-included side 35° 35° 35° 90° √ SSS AAA √ SAS SSA √ ASA √ SAA

  29. Notes - Congruent Triangles These are the triangle congruencies. SSS √ SSS AAA SAS √ SAS SSA √ ASA ASA √ SAA SAA

  30. Theorem 4.8 Hypotenuse –Leg Congruence Theorem (HL) Using Properties of Right triangles If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent.

  31. Using Properties of Right triangles • HL (Hypotenuse - Leg) is not like any of the previous congruence postulates... actually if it was given a name it would be ASS or SSA and earlier we found that this was NOT a congruence postulate.  • HL works ONLY BECAUSE IT IS A RIGHT TRIANGLE!!!!!

  32. SSS If three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent. Methods of Proving Triangles Congruent SAS If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. ASA If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. AAS If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. HL If the hypotenuse and leg of one right triangle are congruent to the corresponding parts of another right triangle, the right triangles are congruent.

  33. Congruent Triangles Name the congruence FRS PQD R P 120° Q F 120° 35° D 35° ASA S

  34. Congruent Triangles Name the congruence QSR FRS R Q 42° 42° F S SSA

  35. Congruent Triangles Name the congruence FRS QSR R 50° Q F 50° S SAS

  36. Congruent Triangles Name the congruence MNR PTB B R SSS N P T WHY? M Names of the triangles in the congruence statement are not in corresponding order.

  37. ASA SSS

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