Geometric Logic Worksheet
A Grade 10 math worksheet focusing on geometric logic, conditional statements, and deductive reasoning in geometry.
Includes
Standards
Topics
Geometric Logic
Name:
Date:
Score:
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?
Related Worksheets
Scaled Copies in Geometry
Explore the properties of scaled copies, including scale factors, corresponding angles, and side lengths. This worksheet is designed for Grade 10 Geometry students.
Heron's Formula Worksheet - Grade 10
Calculate the area of triangles using Heron's Formula with this comprehensive Grade 10 math worksheet.
Hexaflexagon Exploration
Explore the fascinating world of hexaflexagons, their construction, properties, and mathematical principles.
Slicing 3D Figures Worksheet
Explore cross-sections of various 3D geometric figures, including prisms, pyramids, cylinders, and cones, with this Grade 10 math worksheet.
Parts of a Circle Worksheet
Identify and define the various parts of a circle, including radius, diameter, chord, secant, tangent, arc, and sector.
Grade 10 Geometry: Secants
A Grade 10 math worksheet focusing on understanding and applying properties of secants in circles.
Similar Polygons Worksheet
A Grade 10 Math worksheet covering similar polygons, including identifying corresponding sides and angles, and calculating missing side lengths.
Equation of a Circle Worksheet
Practice identifying, writing, and graphing the equation of a circle in standard form.