Worksheet Congruent Triangles Date HR

Transcription

1 Geometry Worksheet ongruent Triangles NME Date HR a) Determine whether the following triangles are congruent. b) If they are, name the triangle congruence (pay attention to proper correspondence when naming the triangles) and then identify the Theorem or Postulate (SSS, SS, S, S, HL) that supports your conclusion. c) e sure to show any additional congruence markings you used in your reasoning. d) If the triangles cannot be proven congruent, state not possible. Then given the reason it is not possible. 1) 2) 3) D EFG EMN 4) 5) 6) STU YZ DE

2 7) 8) 9) KJM NPR STU 10) 11) 12) XYZ DEG HJK 13) 14) 15) STV WXY F

3 16) 17) 18) GJK KLP NSQ 19) 20) 21) LMN STV WXY 22) 23) 24) S E GHJ NPM

4 25) 26) 27) TUV Z EFG Use the given information to mark the diagram appropriately. Name the triangle congruence (pay attention to proper correspondence when naming the triangles) and then identify the Theorem or Postulate (SSS, SS, S, S, HL) that would be used to prove the triangles congruent. If the triangles cannot be proven congruent, state not possible. 28) 29) Given: D ; D Given: JN LM ; NK MK; N M ongruence: DE ongruence: JKN Reason: Reason: 30) 31) Given: D; D Given: SQ and PR bisect each other ongruence: ongruence: RST Reason: Reason:

5 32) Given: GH bisects EGF ; EG FG ongruence: EGH Reason: Now choose one of the problems from and create a flow chart proof. Then transform your flow chart proof into a 2 column proof. Your given will be the Given from the problem and your prove will be the ongruence statement you created.

6 Worksheet # 79 Using PT with Triangle ongruence Name Period 1. Fill in the missing statements and reasons. Given: D, D Prove: D D Statements Reasons Given 2. D Given D 5. ongruence Theorem PT 2. omplete the two-column proof. K Q Given: QK Q, Q bisects KQ Prove: K Statements Reasons Given 2. Q bisects KQ Definition of isector Reflexive Property of ongruence 5. KQ 5. ongruence Postulate Fill in the missing statements and reasons. Given: D, D DE, DE Prove: E Statements Reasons & D are right angles 2. Definition of ll angles are congruent 4. ED DE ongruence D E

7 4. omplete the two-column proof. Given: FJ GH, JFH GHF Prove: FG JH Statements Reasons JFH GHF 2. Given 3. FH HF ongruence Fill in the missing statements and reasons. Given: MN MP, MP PO, MN NO Prove: NOM POM Statements Reasons 1. MP PO, MN NO Definition of Perpendicular Definition of Right Triangle Given ongruence J F P H M O G N 6. omplete the two-column proof. Given: N, N bisects Prove: is an isosceles triangle Statements Reasons N & N are right angles 2. Definition of ll right angles are Given Definition of N 7. ongruence Postulate Definition of Triangle N

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10 Special Segments of Triangles Worksheet: ngle isector, Perpendicular isector, ltitude, Median Name Date Period Name the special segment for #1-4 5) Draw a triangle with an altitude outside the triangle. 6) Fill in the table below: 7. Underline the correct word or phrase to complete each sentence. a. Three or more lines that intersect at a common point are called (parallel/perpendicular/concurrent) lines. b. ny point on the perpendicular bisector of a segment is (parallel to/congruent to/ equidistant from) the endpoints of the segment. c. (n) (altitude/angle bisector/median/perpendicular bisector) of a triangle is a segment drawn from a vertex of a triangle perpendicular to the line containing the opposite side. d. The point of concurrency of the three perpendicular bisectors of a triangle is called the (orthocenter/circumcenter/incenter/centriod). e. The point of concurrency of the three angle bisectors of a triangle is called the (orthocenter/ circumcenter/ incenter/ centriod).

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12 Exterior ngles of Triangles Worksheet 1. In the diagram, vertex of isosceles measures 94 o. What is the measure of D? 2. In PQR, the measure of P is twice the measure of Q. If an exterior angle at vertex R has a measure of 120, find m Q. D 3. n exterior angle at the base of an isosceles triangle is always: (1) right (3) acute (2) obtuse (4) equal to the base 4. In RST, S is a right angle. The exterior angle at vertex S is: (1) right (3) acute (2) obtuse (4) straight " 5. In, m = 40 and m = 60. The degree measure of the exterior angle at vertex is: (1) 40 (3) 60 (2) 80 (4) Side of is extended through to D. If m D = 108 " and m = 2m, is (1) right (3) obtuse (2) isosceles (4) scalene 7. In the figure, D is an exterior angle of m = ( ) " x and m = 80 ", find x.. If m D = ( 3 ) " x, D 8. In the drawn below, D is drawn such that D. If m = 50 o and m D is 70 o more than D, then the measure of is? D 9. In, m is four times as large as m. n exterior angle at measures 125 o. Find the degree measure of. Geometry Triangle Inequalities

13 10. In isosceles, ( x ). If m ( 6x 10) = + and the m = , find the measure of an exterior angle at vertex. #$% #$$% " " 11. If EF & GH, m x = 68 and m y = 117, find m z. E y x F G z H 12. Using the diagram, find the value of x. 13. Using the diagram, find the value of x. 12x - 8 ( ) 12x - 32 ( ) 4x + 6 ( ) 7x - 6 ( ) 5x - 5 ( ) 14. (H) In an isosceles triangle, drawn at vertex ( x 27) 2, m ( 7 ) = +. Find the m. = x x and the exterior angle 15. In the diagram of and m D ( 6x 89) 2, m ( x 5x 10) = +. Find m = +, ( ). m = 3x, D 16. (H) In EFG 2, side EF is extended through F to H. If m G ( x 6x 9) = ( x ) and m GFH ( 9x 25) m E 3 6 =, = +. Find x. Round to the nearest hundredth. Geometry Triangle Inequalities