Five-Minute Check (over Lesson 1–4) Mathematical Practices Then/Now New Vocabulary Key Concept: Special Angle Pairs Example 1: Real-World Example: Identify Angle Pairs Key Concept: Angle Pair Relationships Example 2: Angle Measure Key Concept: Perpendicular Lines Example 3: Perpendicular Lines Key Concept: Interpreting Diagrams Example 4: Interpret Figures Lesson Menu

Refer to the figure. Name the vertex of 3. A. A B. B C. C D. D 5-Minute Check 1

Refer to the figure. Name a point in the interior of ACB. A. G B. D C. B D. A 5-Minute Check 2

Refer to the figure. Which ray is a side of BAC? A. DB B. AC C. BD D. BC 5-Minute Check 3

Refer to the figure. Name an angle with vertex B that appears to be acute. A. ABG B. ABC C. ADB D. BDC 5-Minute Check 4

Refer to the figure. If bisects ABC, mABD = 2x + 3, and mDBC = 3x – 13, find mABD. A. 41 B. 35 C. 29 D. 23 5-Minute Check 5

OP bisects MON and mMOP = 40°. Find the measure of MON. 5-Minute Check 6

Mathematical Practices 5 Use appropriate tools strategically. 6 Attend to precision. Content Standards G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. MP

You measured and classified angles. Identify and use special pairs of angles. Identify perpendicular lines. Then/Now

adjacent angles linear pair vertical angles complementary angles supplementary angles perpendicular Vocabulary

Concept

Sample Answers: PIQ and QIS, PIT and TIS, QIU and UIT Identify Angle Pairs A. ROADWAYS Name an angle pair that satisfies the condition two angles that form a linear pair. A linear pair is a pair of adjacent angles whose noncommon sides are opposite rays. Sample Answers: PIQ and QIS, PIT and TIS, QIU and UIT Example 1

Sample Answers: PIU and RIS, PIQ and TIS, QIR and TIU Identify Angle Pairs B. ROADWAYS Name an angle pair that satisfies the condition two acute vertical angles. Vertical angles are two nonadjacent angles formed by two intersecting lines. Acute angles are angles that measure less than 90°. Sample Answers: PIU and RIS, PIQ and TIS, QIR and TIU Example 1

A. Name two adjacent angles whose sum is less than 90. A. CAD and DAE B. FAE and FAN C. CAB and NAB D. BAD and DAC Example 1a

B. Name two acute vertical angles. A. BAN and EAD B. BAD and BAN C. BAC and CAE D. FAN and DAC Example 1b

Concept

Angle Measure ALGEBRA Find the measures of two supplementary angles if the measure of one angle is 6 less than five times the measure of the other angle.   Example 2

Solve 6x – 6 = 180 Simplify. 6x = 186 Add 6 to each side. Angle Measure Solve 6x – 6 = 180 Simplify. 6x = 186 Add 6 to each side. x = 31 Divide each side by 6. Example 2

Use the value of x to find each angle measure. mA = x mB = 5x – 6 = 31 = 5(31) – 6 or 149 Check Add the angle measures to verify that the angles are supplementary. mA + mB = 180 31 + 149 = 180 180 = 180    Example 2

ALGEBRA Find the measures of two complementary angles if one angle measures six degrees less than five times the measure of the other. A. 1°, 1° B. 21°, 111° C. 16°, 74° D. 14°, 76° Example 2

Concept

ALGEBRA Find x and y so that KO and HM are perpendicular. Perpendicular Lines ALGEBRA Find x and y so that KO and HM are perpendicular. Example 3

84 = 12x Subtract 6 from each side. 7 = x Divide each side by 12. Perpendicular Lines 90 = (3x + 6) + 9x Substitution 90 = 12x + 6 Combine like terms. 84 = 12x Subtract 6 from each side. 7 = x Divide each side by 12. Example 3

84 = 3y Subtract 6 from each side. 28 = y Divide each side by 3. Perpendicular Lines To find y, use mMJO. mMJO = 3y + 6 Given 90 = 3y + 6 Substitution 84 = 3y Subtract 6 from each side. 28 = y Divide each side by 3. Answer: x = 7 and y = 28 Example 3

A. x = 5 B. x = 10 C. x = 15 D. x = 20 Example 3

Concept

A. Determine whether each statement can be Interpret Figures A. Determine whether each statement can be assumed from the figure below. Explain. mVYT = 90 Example 4

B. Determine whether each statement can be Interpret Figures B. Determine whether each statement can be assumed from the figure below. Explain. TYW and TYU are supplementary. A linear pair is a pair of adjacent angles whose noncommon sides are opposite rays. Linear pairs are also supplementary. Answer: Yes, they form a linear pair of angles. Example 4

C. Determine whether each statement can be Interpret Figures C. Determine whether each statement can be assumed from the figure below. Explain. VYW and TYS are adjacent angles. Adjacent angles are two angles that lie in the same plane and have a common vertex and a common side, but no common interior points. Answer: No, they do not share a common side. Example 4

A. Determine whether the statement mXAY = 90 can be assumed from the figure. A. yes B. no Example 4a

B. Determine whether the statement TAU is complementary to UAY can be assumed from the figure. A. yes B. no Example 4b

C. Determine whether the statement UAX is adjacent to UXA can be assumed from the figure. A. yes B. no Example 4c