SCS G.CO.C.8 Geometry Proof

Consider the figure, where parallel lines r and s are cut by a transversal, t.

The student then proves that ∠4 ≅ ∠8. The table shows the steps.

Which justifications complete the proof?

• Vertical Angles Theorem, Corresponding Angles Postulate

• Alternate Interior Angles Theorem, Corresponding Angles Postulate

• Vertical Angles Theorem,

  Alternate Interior Angles Theorem

• Corresponding Angles Postulate,

  Alternate Interior Angles Theorem

Which statement is true?

• Complementary angles always add up to 90°.

• Complementary angles always add up to 180°.

• Complementary angles are always congruent.

• Complementary angles are always vertical angles.

In the diagram below Points G, H, and I are collinear. Which conjecture is not necessarily true?

• ∠GHK ≅ ∠KHI

• m∠GHJ + m∠JHI = 180°

• ∠GHJ and ∠JHI form a linear pair

• ∠GHK and ∠JHI are vertical angles

• If two parallel lines are cut by a transversal, the alternate interior angles are congruent.

• If two parallel lines are cut by a transversal, the alternate exterior angles are congruent.

• If two parallel lines are cut by a transversal, the corresponding angles are congruent.

• If two parallel lines are cut by a transversal, the vertical angles are congruent.

Which conjecture must be true?

• If two angles are adjacent angles, then the angles are supplementary.

• If two congruent angles are supplementary, then the angles are right angles.

• If two congruent angles have a common vertex, then the angles are vertical angles.

• If two angles are both acute angles, then the sum of the angle measures is less than 90°.

If two angles add to 90 degrees, then they are complementary.​ (a)  

• True
• False

α and β are supplementary angles.  If α = 130⁰, then β = _______

• 50⁰
• 40⁰
• -40⁰
• None of the above

Tags

CCSS.7.G.B.5

If angle ∠ABD is 67°. What is ∠DBC?

• 180°
• 90°
• 67°
• 23°