Download presentation

Presentation is loading. Please wait.

1
**2.5 Reasoning in Algebra and Geometry**

Objective: To connect reasoning in algebra and geometry

2
**Properties of Equality**

Let a, b, and c be any real number. Addition If a = b, then a + c = b + c Subtraction If a = b, then a – c = b – c Multiplication If a = b, then a ∙ c = b ∙ c Division If a = b and c ≠ 0, then a/c = b/c Reflexive a = a Symmetric If a = b, then b = a. Transitive If a = b and b = c, then a = c. Substitution If a = b, then b can replace a in any expression Distributive a(b + c) = ab + ac a(b – c) = ab – ac

3
**Justify Steps When Solving**

M C A x° (2x + 30)° What is the value of x? ∠𝐴𝑂𝑀 and ∠𝑀𝑂𝐶 Angles that form a linear are supplementary pair are supplementary 𝑚∠𝐴𝑂𝑀 + 𝑚∠𝑀𝑂𝐶 = Definition of suppl. Angles (2x + 30) + x = Substitution Property 3x + 30 = Distributive Property 3x = Subtraction Prop. of Eq. X = Division Prop. of Eq.

4
**Try again. What is the value of x? Given: 𝐴𝐵 bisects ∠𝑅𝐴𝑁 B R N A x°**

5
Extra Practice D F E C x° (2x – 15)° What is the value of x?

6
**Equality and Congruence**

Reflexive Property 𝐴𝐵 ≅ 𝐴𝐵 ∠𝐴≅∠𝐴 Symmetric Property If 𝐴𝐵 ≅ 𝐶𝐷 , then 𝐶𝐷 ≅ 𝐴𝐵 If ∠𝐴≅∠𝐵, then ∠𝐵≅∠𝐴 Transitive Property If 𝐴𝐵 ≅ 𝐶𝐷 and 𝐶𝐷 ≅ 𝐸𝐹 , then 𝐴𝐵 ≅ 𝐸𝐹 If ∠𝐴≅∠𝐵 and ∠𝐵≅∠𝐶, then ∠𝐴≅∠𝐶 If ∠𝐵≅∠𝐴 and ∠𝐵≅∠𝐶, then ∠𝐴≅∠𝐶

7
**Using Equality and Congruence**

What property of equality or congruence is used to justify going from the first statement to the second statement? 2x + 9 = 19 2x = 10 B. ∠𝑂≅∠𝑊 and ∠𝑊≅∠𝐿 ∠𝑂≅∠𝐿 C. 𝑚∠𝐸=𝑚∠𝑇 𝑚∠𝑇=𝑚∠𝐸

8
Proof Proof – convincing argument that uses deductive reasoning; logically shows why a conjecture is true Two-column proof – lists each statement on the left and the justification/reason on the right

9
**Here we go… Given: 𝑚∠1=𝑚∠3 Prove: 𝑚∠𝐴𝐸𝐶=𝑚∠𝐷𝐸𝐵 What do we know?**

What do we need to do? What is our plan?

10
𝑚∠1=𝑚∠3 Given 𝑚∠2=𝑚∠2 Reflexive Prop of = 𝑚∠1+𝑚∠2=𝑚∠3+𝑚∠2 Addition Prop of = 𝑚∠1+𝑚∠2=𝑚∠𝐴𝐸𝐶 Angle Add. Post. 𝑚∠3+𝑚∠2=𝑚∠𝐷𝐸𝐵 𝑚∠𝐴𝐸𝐶=𝑚∠𝐷𝐸𝐵 Substitution Prop

11
Again… Given: 𝐴𝐵 ≅ 𝐶𝐷 Prove: 𝐴𝐶 ≅ 𝐵𝐷 A C B D

12
Page #5-23 odd

Similar presentations

© 2021 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google