Day 36 Review for TEST 1-2 (geom)

Which pair of adjacent angles serve as a counterexample to the statement that adjacent angles are supplementary?

• A

• B

• C

• D

Given the biconditional: Two lines are perpendicular if and only if they intersect at right angles.

Write the conditional statement that could be written from the biconditional. What is the converse of that conditional statement?

• Conditional statement: If two lines intersect at right angles, then they are perpendicular.

  Converse: If two lines are not perpendicular, then they do not intersect at right angles.

• Conditional statement: If two lines are perpendicular, then they intersect at right angles.

  Converse: If two lines do not intersect at right angles, then they are not perpendicular.

• Conditional statement: If two lines intersect at right angles, then they are perpendicular.

  Converse: If two lines are perpendicular, then they intersect at right angles.

• Conditional statement: If two lines are perpendicular, then they intersect at right angles.

  Converse: If two lines intersect at right angles, then they are perpendicular.

Answer explanation

Rewrite the definition of congruent segments as a single biconditional statement. Definition: If two line segments have the same length, then they are congruent segments.

• If two line segments are congruent, then they have the same length.

• If two line segments are not congruent, then they don’t have the same length.

• Two line segments have the same length if and only if they are congruent segments.

• Two line segments do not have the same length if and only if they are not congruent segments.

Answer explanation

biconditional statements are written with "if and only if" only when the conditional and converse are both true

What is the inverse of the statement, “If a parallelogram has a right angle, then the parallelogram is a rectangle”?

• If a parallelogram is a rectangle, then the parallelogram has a right angle.

• If a parallelogram is not a rectangle, then the parallelogram does not have right angle.

• If a parallelogram does not have a right angle, then the parallelogram is not a rectangle.

• If a parallelogram has a right angle, then the parallelogram is not a rectangle.

Answer explanation

For inverse...think, "inverse operations"...the opposite of addition is subtraction, so change the positive phrasing to negative phrasing

Given the statement “If two triangles are not similar, their corresponding angles are not congruent”, write the inverse, converse, and contrapositive statements.

• Inverse: If two triangles are similar, their corresponding angles are congruent.

  Converse: If the corresponding angles are congruent, then the two triangles are similar.

  Contrapositive: If the corresponding angles are not congruent, then the two triangles are not similar.

• Inverse: If the corresponding angles are congruent, then the two triangles are similar.

  Converse: If two triangles are similar, their corresponding angles are congruent.

  Contrapositive: If the corresponding angles are not congruent, then the two triangles are not similar.

• Inverse: If the corresponding angles are not congruent, then the two triangles are not similar.

  Converse: If two triangles are similar, their corresponding angles are congruent.

  Contrapositive: If the corresponding angles are congruent, then the two triangles are similar.

• Inverse: If two triangles are similar, their corresponding angles are congruent.

  Converse: If the corresponding angles are not congruent, then the two triangles are not similar.

  Contrapositive: If the corresponding angles are congruent, then the two triangles are similar.

Answer explanation

Which of the options best describes a counterexample to the assertion below?

“Two lines in a plane always intersect in exactly one point.”

• coplanar lines

• parallel lines

• perpendicular lines

• intersecting lines

Answer explanation

A counterexample proves the statement false with just a single example!

Parallel lines never intersect!

Which situation would provide a counterexample to this statement?

“Adjacent angles are never supplementary.”

• A line that is parallel to two parallel lines.

• A transversal that forms 45° angle with two parallel lines.

• <A plus <B = 180; <A and <B are adjacent

• A line that has a slope that is the reciprocal of the slopes of two parallel lines.

Answer explanation

A counterexample proves the statement false with just a single example!

Here, alternate interior angles would be supplementary because 90+90=180.

Which of the options best describes a counterexample to the assertion below?

“If one pair of opposite sides of a quadrilateral is congruent, then the quadrilateral is a parallelogram.”

• Isosceles trapezoid

• Rectangle

• Rhombus

• Square

Answer explanation

A counterexample proves the statement false with just a single example!

Like in the diagram, an isosceles trapezoid is a quadrilateral that has one pair of parallel sides, but only one pair, so it isn't a parallelogram.

What is the contrapositive of the following conditional?

If a point is in the first quadrant, then its coordinates are positive.

Choose the correct answer from each drop-down menu to complete the statement.​ ​ ​

• If the coordinates are not positive, then the point is not in the first quadrant
• If the coordinates are positive, then the point is in the first quadrant.
• If a point is not in the first quadrant, then its coordinates are positive.
• If a point is in the first quadrant, then its coordinates are negative.

What is the converse of the following conditional?

If two angles measure 180º, then the two angles are supplementary angles.

Choose the correct answer from each drop-down menu to complete the statement.

• If two angles are not supplementary angles, then the two angles do not measure 180º.
• If two angles are not supplementary angles, then the two angles measure 180º.
• If two angles are supplementary angles, then the two angles measure 180º.
• If two angles measure 180º, then the two angles are not supplementary angles.