Ezekiel 36: 26-27

1. 26. “I will give you a new heart and put a new spirit within you; I will take the heart of stone out of your flesh and give you a heart of flesh. 27. “ I will put My spirit within you and cause you to walk in My statutes, and you will keep My judgments and do them. Ezekiel 36: 26-27

2. CONDITIONAL STATEMENTS BY: JEREMIAH A. ALTAR

3. Your Goals • Write the if-then form of a given conditional statement. • Write the converse of a conditional statement. • Evaluate the converse of a conditional statement.

4. Conditional Statements • Many mathematical concepts are written or expressed as conditional statements. These includes axioms or postulates, theorems, corollaries and even mathematical or scientific laws. • But then, what is a conditional statement?

5. Conditional Statements • Conditional Statements or simply conditionals are statements written in the “if – then” form, wherein: * the if statement is the HYPOTHESIS * the then statement is the CONCLUSION EXAMPLE: If you are 18 years old, then you can vote in the national election CONCLUSION HYPOTHESIS

6. Other Examples 1. If two segments are congruent, HYPOTHESIS then they have the same measure. CONCLUSION 2. If x = 5, then x2 = 25 HYPOTHESIS CONCLUSION 3. If y = 3, then 4y = 12 HYPOTHESIS CONCLUSION

7. More About Conditionals • Some conditional statements do not appear in the “if-then” form, consider the following: Conditional: Congruent segments have equal lengths. If –then form: If two segments are congruent, then they have equal lengths.

8. Other Examples Conditional: Acute angles measure is less than 900 If –then form: If two angles are acute angles, then their measure is less than 900. Conditional: Right triangles have one right angle. If –then form: If two triangles are right triangles, then they have one right angle.

9. Converse of a Conditional • Another “if – then” statement can be formed by interchanging the hypothesis and the conclusion of a conditional statement. The new statement is called CONVERSE. EXAMPLE: Conditional: If you are 18 years old, then you can vote in the national election CONCLUSION HYPOTHESIS Converse: If you can vote in the national election, then you are 18 years old. CONCLUSION HYPOTHESIS NOTE: NOT ALL CONVERSE STATEMENTS ARE TRUE!

10. Other Examples If x = 5, then x2 = 25 Conditional: Ifx2 = 25, then x = 5 Converse: If y = 3, then 4y = 12 Conditional: Converse: If4y = 12, then y = 3

11. Let’s Try the Following: • Write the if – then form and the converse of the following conditional statement. Evaluate if its converse is true or not true. Conditional: Right angles measure are congruent. If –then form: If two angles are right angles, then their measures are congruent. Converse: If the measures of two angles are congruent, then they are right angles. Evaluation: the converse is NOT TRUE

12. QUIZ • Write the if – then form and the converse of the following conditional statements. Evaluate if its converse is true or not true. 1. Collinear points lie on the same line. 2. A triangle contains exactly three interior angles.

13. ANSWER for No. 1 Conditional: If two points are collinear points, then they lie on the same line. Converse: If two points lie on the same line, then they are collinear points. Evaluation: True

14. ANSWER for No. 2 Conditional: If a polygon is a triangle, then it has exactly three interior angles Converse: If a polygon has exactly three interior angles, then it is a triangle Evaluation: True

15. Assignment • What are the properties of equality? • Give an example for each property.