5/06 Lesson 15-6 Problem Solving Make &Test Generalizations

Which of these generalizations is true?

• All squares are rectangles.

• All rectangles are square.

• All quadrilaterals are trapezoids.

• All rectangles are trapezoids.

Which of these generalizations is true?

• All triangles have 4 sides, 4 angles, and 4 vertices.

• All quadrilaterals have 4 sides, 4 angles, and 4 vertices.

• All pentagons have 6 sides, 6 angles, and 6 vertices.

• All octagons have 7 sides, 7 angles, and 7 vertices.

Which of these generalizations is true?

• Perpendicular lines are parallel lines.

• Parallel Lines are perpendicular lines.

• Parallel lines will always intersect.

• Perpendicular lines can never be parallel lines.

Which of these generalizations is FALSE?

• A rhombus can be a parallelogram.

• A parallelogram can be a quadrilateral.

• Trapezoids can be squares.

• A square can be a rhombus, rectangle, parallelogram, and a quadrilateral.

Test the generalization and state whether it appears to be correct or incorrect. If incorrect, give an example to support why.

GENERALIZATION:

The sum of all the angles of a quadrialeral is 300 degrees.

• Correct

• Incorrect, a square has 4 right angles. Right angles equal 90 degrees each. 4 x 90 = 360.

• Incorrect, a square has 4 right angles. Right angles equal 45 degrees each. 4 x 45= 180.

• Incorrect, a trapezoid has 4 right angles. Right angles equal 90 degrees each. 4 x 90 = 360.

Test the generalization and state whether it appears to be correct or incorrect. If incorrect, give an example to support why.

GENERALIZATION:

All triangles have at least one right angle.

• Correct

• Incorrect, an actute triangle has an angle that is greater than 90 degrees but less than 180 degrees (obtuse angle) and two acute angles.

• Incorrect, an acute triangle has an angle that is greater than 90 degrees but less than 180 degrees (obtuse angle) and two acute angles.

• Incorrect, an obtuse triangle has an angle that is greater than 90 degrees but less than 180 degrees (obtuse angle) and two acute angles.