1 / 21

2.2b: Exploring Congruent Triangles with Proofs

2.2b: Exploring Congruent Triangles with Proofs. CCSS. A proof is an argument that uses logic, definitions, properties, and previously proven statements to show that a conclusion is true. An important part of writing a proof is giving justifications to show that every step is valid.

allistair-emerson
Download Presentation

2.2b: Exploring Congruent Triangles with Proofs

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 2.2b: Exploring Congruent Triangles with Proofs CCSS

  2. A proof is an argument that uses logic, definitions, properties, and previously proven statements to show that a conclusion is true. An important part of writing a proof is giving justifications to show that every step is valid.

  3. Division Property of Equality Example 1: Solving an Equation in Algebra Solve the equation 4m – 8 = –12. Write a justification for each step. 4m – 8 = –12 Given equation +8+8Addition Property of Equality 4m = –4 Simplify. m = –1 Simplify.

  4. Solve the equation . Write a justification for each step. Given equation Multiplication Property of Equality. t = –14 Simplify. Check It Out! Example 1

  5. Example 3: Solving an Equation in Geometry Write a justification for each step. NO = NM + MO Segment Addition Post. 4x – 4 = 2x + (3x – 9) Substitution Property of Equality 4x – 4 = 5x – 9 Simplify. –4 = x – 9 Subtraction Property of Equality 5 = x Addition Property of Equality

  6.  Add. Post. mABC = mABD + mDBC Check It Out! Example 3 Write a justification for each step. 8x°=(3x + 5)°+ (6x – 16)° Subst. Prop. of Equality 8x = 9x – 11 Simplify. –x = –11 Subtr. Prop. of Equality. x = 11 Mult. Prop. of Equality.

  7. Remember! Numbers are equal (=) and figures are congruent ().

  8. Example 4: Identifying Property of Equality and Congruence Identify the property that justifies each statement. A. QRS  QRS B. m1 = m2 so m2 = m1 C. AB  CD and CD  EF, so AB EF. D. 32° = 32° Reflex. Prop. of . Symm. Prop. of = Trans. Prop of  Reflex. Prop. of =

  9. Check It Out! Example 4 Identify the property that justifies each statement. 4a. DE = GH, so GH = DE. 4b. 94° = 94° 4c. 0 = a, and a = x. So 0 = x. 4d. A  Y, so Y  A Sym. Prop. of = Reflex. Prop. of = Trans. Prop. of = Sym. Prop. of 

  10. Ex. Identify the property that justifies each statement. 3. x = y and y = z, so x = z. 4. DEF  DEF 5. ABCD, so CDAB. Trans. Prop. of = Reflex. Prop. of  Sym. Prop. of 

  11. 2-Column Proof • Numbered statements and corresponding reasons in a logical order organized into 2 columns. statements reasons 1. 1. 2. 2. 3. 3. etc.

  12. 2-Column Proof (Con’t) statements reasons • You can only use: • Given • Definitions • Postulates • Theorems • Properties

  13. Statements PQ=2x+5, QR=6x-15, PR=46. 2. PQ+QR=PR 3. 2x+5+6x-15=46 4. 8x-10=46 5. 8x=56 6. x=7 Reasons Given Seg Add Post. Subst. prop of = Simplify Add prop of = Division prop of = Ex: Given: PQ=2x+5 QR=6x-15 PR=46 Prove: x=7 P Q R

  14. Statements Q is midpt of PR PQ=QR PQ+QR=PR QR+QR=PR 2QR=PR QR= PQ= Reasons Given Defn. of midpt Seg Add. post Subst. prop of = Simplify Division prop of = Subst. prop Ex: Given: Q is the midpoint of PR. Prove: PQ and QR =

  15. Example– Given: HA || KS Prove: Reasons Statement Given 1 HA || KS, 1 Alt. Int. Angles are congruent 2 2 Vertical Angles are congruent 3 3 4 ASA Postulate 4

  16. Example Given: Prove: Statement Reason 1) Given 1)

  17. Example Given: Prove: Statement Reason 1) Given 1) 2) 2)

  18. Example Given: Prove: Statement Reason 1) Given 1) 2) 2)

  19. Given: Prove: Reasons Statement Given 1 , 1

More Related