Properties, Postulates, Definitions, and Theorems

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.

• 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

Identify the correct reason for each statement.

• Substitution postulate

• Definition of angle bisector

• Angle addition postulate

• Angle bisector theorem

Identify the correct reason for each statement.

• Substitution postulate

• Definition of angle bisector

• Angle addition postulate

• Angle bisector theorem

• 21°

• Cannot be determined

• 63°

• 42°

Two intersecting lines are shown in the diagram. Solve for x.

• 𝑥=10

• 𝑥=−10

• 𝑥≈7.89

• 𝑥≈1.83

Given three intersecting lines, which of the following statements are true? Select all that apply.

• ∠4 ≅ ∠1

• ∠6 and ∠2 are vertical angles.

• ∠2 is a 180° rotation of ∠5 about point G.

• ∠4 and ∠3 are adjacent angles.

Classify the angle

• Straight angle

• Acute angle

• Obtuse angle

• Right angle

If the ray HK is bisecting ∠GHJ, then what reason would you use to say ∠GHK is congruent to ∠KHJ?

• Definition of Midpoint

• Definition of Angle Bisector

• Definition of Congruent

• Definition of Segment Bisector

If angles are congruent, then the measures of the angles are equal. Identify the converse.

• If the measures of the angles are equal, then the angles are congruent.

• If angles are not congruent, then the measures of the angles are not equal.

• If the measures of the angles are not equal, then the angles are not congruent.

• If the angles are not congruent, then the measure of the angles are equal.