Geometry Proofs Theorems Postulates and Properties

State the theorem illustrated by the diagram.

State the theorem illustrated by the diagram.

State the theorem illustrated by the diagram.

State the postulate illustrated by the diagram.

How many lines drawn in the figure contain point Z?

• 1

• 2

• 3

• 4

Which of the following can be used as reasons in a proof? Select all that apply.

• Definitions

• Algebraic properties

• Postulates

• Theorems

• Conjectures

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

Fill in the blank to give a reason for the statement below. You may refer to the Properties of Equality shown. If m∠1=m∠2 and m∠2=m∠3, then m∠1=m∠3 by the__________ property of equality.

• addition

• subtraction

• symmetric

• transitive

• multiplication

• 21°

• Cannot be determined

• 63°

• 42°