# Deductive Reasoning - Law of Detachment - Law of Syllogism

## Free Geometry Worksheet - Deductive Reasoning - Law of Detachment - Law of Syllogism

**Lesson:**

**Subject:**

**Description:**

Problems require students to use the law of detachment (If p→q is a true statement and p is true, then q is true) and the law of syllogism (If p→q and q→r are true statements, then p→r is a true statement) to draw conclusions from given statements.

**# of Problems:** 9

**# of Pages:** 3

**Answer Key?:** Yes

### Sample Problems from Worksheet

(Worksheet pictures and diagrams not shown)

Tutor-USA.com Worksheet

Geometry

Law of Detachment – Law of Syllogism

1) The law of detachment states that if a conditional is true and its hypothesis is true, then its ______ must also be true.

Use the Law of Detachment to draw a conclusion if possible.

2) If two lines are parallel, then they do not intersect Line a is parallel to line b.

3) If three points lie on the same line, then they are collinear.

Points A, B, and C lie on line l.

4) If the measures of two angles have a sum of 90 degrees, then the angles are complementary.

m∠1+ m∠2 = 90

5) If two figures are congruent, then their areas are equal.

The area of ABCD equals the area of WXYZ