HG M2 D1 ET Logic and Reasoning

Underline the hypothesis and italicize the conclusion in each statement.

• If your dog eats Purina, then he’ll stay happy and healthy.

• If your dog eats Purina, then he’ll stay happy and healthy.

• If your dog eats Purina, then he’ll stay happy and healthy.

• If your dog eats Purina, then he’ll stay happy and healthy.

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."

What is the converse of this statement?

• If a polygon is not a quadrilateral, then it is not a trapezoid.

• If a polygon is not a trapezoid, then it is not a quadrilateral.

• If a polygon is a trapezoid, then it is a quadrilateral.

• A rectangle is also a quadrilateral.

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."

What is the inverse of this statement?

• If the polygon is not a quadrilateral, then it is not a trapezoid.

• If the polygon is not a trapezoid, then it is not a quadrilateral.

• If the polygon is a trapezoid, then it is a quadrilateral.

• A rectangle is also a quadrilateral.

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."

What is the contrapositive of this statement?

• If a polygon is a trapezoid, then it is a quadrilateral.

• If a polygon is not a quadrilateral, then it is not a trapezoid.

• If a polygon is not a trapezoid, then it is not a quadrilateral.

• A rectangle is also a quadrilateral.

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."

What is a counterexample of this statement?

• If a polygon is a trapezoid, then it is a quadrilateral.

• If a polygon is not a quadrilateral, then it is not a trapezoid.

• If a polygon is not a trapezoid, then it is not a quadrilateral.

• A rectangle is also a quadrilateral.

If two angles form a linear pair, what can you conclude about the angles?

• The two angles are congruent.

• The two angles are complementary.

• The two angles are supplementary.

• The two angles are right angles.

Earlier in this topic, you proved the Common Segment Theorem. Do you think you could prove a Common Angle Theorem? Using the diagram, what do you think that theorem would state? Select all that apply.

Hint: Read each statement. Which statements deal with a shared angle?

• If K and M are in the interior of ∠𝖧𝖨𝖩,

  then 𝗆∠𝖧𝖨𝖪+𝗆∠𝖪𝖨𝖬+𝗆∠𝖩𝖨𝖬=𝗆∠𝖧𝖨𝖩.

• If ∠𝖧𝖨𝖪≅∠𝖩𝖨𝖬,

  then ∠𝖧𝖨𝖬≅∠𝖩𝖨𝖪.

• If ∠𝖧𝖨𝖬≅∠𝖩𝖨𝖪,

  then ∠𝖧𝖨𝖪≅∠𝖩𝖨𝖬.

• If ∠𝖧𝖨𝖪≅∠𝖩𝖨𝖬,

  then ∠𝖪𝖨𝖬≅∠𝖬𝖨𝖪.

Select the response that justifies the given statement:

XP + PY = XY

• Addition property

• Subtraction property

• Segment Addition postulate

• Angle addition postulate

What do you call an "If , then" sentence?

• Conditioner

• Conditional

• Counterexample

• Classical

Rewrite this sentence as a conditional:

All negative numbers are less than 0.

• Some negative numbers are less than 0.

• All numbers less than 0 are negative numbers.

• If a number is negative, then it is less than 0.

• If a number is positive, then it is greater than 0.