Geometric Logic Worksheet
A Grade 10 math worksheet focusing on geometric logic, conditional statements, and deductive reasoning in geometry.
Includes
Standards
Topics
Geometric Logic
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Carefully read each question and follow the instructions. Show all your work where applicable.
1. Which of the following is the contrapositive of the statement: 'If a polygon is a square, then it has four equal sides'?
If a polygon has four equal sides, then it is a square.
If a polygon is not a square, then it does not have four equal sides.
If a polygon does not have four equal sides, then it is not a square.
A polygon is a square if and only if it has four equal sides.
2. Given the statements: P: A triangle is equilateral. Q: A triangle is equiangular. Which of the following represents 'If a triangle is not equiangular, then it is not equilateral'?
P → Q
Q → P
~Q → ~P
~P → ~Q
3. The statement 'If two angles are vertical angles, then they are congruent' is a conditional statement. The hypothesis is and the conclusion is .
4. The converse of 'If a figure is a rectangle, then it has four right angles' is .
5. The inverse of 'If a triangle is isosceles, then it has two equal sides' is .
6. The inverse of a conditional statement always has the same truth value as the original statement.
True
False
7. Write a conditional statement, its converse, inverse, and contrapositive using the terms 'parallel lines' and 'never intersect'.
Conditional:
Converse:
Inverse:
Contrapositive:
8. Consider the following statements:
Premise 1: All squares are rectangles.
Premise 2: Figure A is a square.
What conclusion can be drawn from these premises using deductive reasoning?