paolo30pante
Answered

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RECAP
Directions: Identify what is being described in each item. Write your answer on the space
provided
1. Two coplanar angles that have a common side between them but have no
interior points in common
2. Pair of angles whose sum is equal to 180 degrees
3. Nonadjacent angles formed by two intersecting lines
4. Pair of angles which are adjacent and supplementary to each other
5. Pair of angles whose sum is equal to 90 degrees​

Sagot :

cherrylgeverola1989

Step-by-step explanation:

There are some special relationships between "pairs" of angles.

bullet Adjacent Angles are two angles that share a common vertex, a common side, and no common interior points. (They share a vertex and side, but do not overlap.)

adjangles

∠1 and ∠2 are adjacent angles.

∠ABC and ∠1 are NOT adjacent angles.

(∠ABC overlaps ∠1.)

divider

bullet A Linear Pair is two adjacent angles whose non-common sides form opposite rays.

linearpair

∠1 and ∠2 form a linear pair.

The line through points A, B and C is a straight line.

∠1 and ∠2 are supplementary.

theorem

If two angles form a linear pair, the angles are supplementary.

A linear pair forms a straight angle which contains 180º, so you have 2 angles whose measures add to 180, which means they are supplementary.

theorem

If two congruent angles form a linear pair, the angles are right angles.

If two congruent angles add to 180º, each angle contains 90º, forming right angles.

divider

bullet Vertical Angles are two angles whose sides form two pairs of opposite rays (straight lines).

vertical

Vertical angles are located across from one another in the corners of the "X" formed by the two straight lines.

∠1 and ∠2 are vertical angles.

∠3 and ∠4 are vertical angles.

Vertical angles are not adjacent.

∠1 and ∠3 are not vertical angles (they are a linear pair).

Vertical angles are always equal in measure.

theorem

Vertical angles are congruent.

Vertical angles, such as ∠1 and ∠2, form linear pairs with the same angle, ∠4, giving m∠1 + m∠4 = 180 and m∠2 + m∠4 = 180. With substitution, m∠1 = m∠2 and they are congruent.

divider

bullet Complementary Angles are two angles the sum of whose measures is 90º.

comp

Complementary angles can be placed so they form perpendicular lines, or they may be two separate angles.

∠1 and ∠2 are complementary.

∠P and ∠Q are complementary.

perp

theorem

Complements of the same angle, or congruent angles, are congruent.

If m∠a is complementary to the m∠b, and m∠c is complementary to m∠b, then

m∠a = m∠c. Consider m∠a = 60º, m∠b = 30º and m∠c = 60º.

theorem

The acute angles of a right triangle are complementary.

The sum of the angles in a triangle add to 180º. After subtracting 90º for the right angle, there are 90º left for the two acute angles, making them complementary.

divider

bullet Supplementary Angles are two angles the sum of whose measures is 180º.

supp

Supplementary angles can be placed so they form a linear pair (straight line), or they may be two separate angles.

∠1 and ∠2 are supplementary.

∠P and ∠Q are supplementary.

The line through points A, B and C is a straight line.

theorem

Supplements of the same angle, or congruent angles, are congruent.

If m∠a is supplementary to the m∠b, and m∠c is supplementary to m∠b, then

m∠a = m∠c. Consider m∠a = 60º, m∠b = 120º and m∠c = 60º.

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