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Splash Screen. Five-Minute Check (over Lesson 1–4) CCSS 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
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Five-Minute Check (over Lesson 1–4) CCSS 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
A.DB B.AC C.BD D.BC Refer to the figure. Which ray is a side of BAC? 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, mABD = 2x + 3, andmDBC = 3x – 13, find mABD. A. 41 B. 35 C. 29 D. 23 5-Minute Check 5
OP bisects MON and mMOP = 40°. Find the measure of MON. A. 20° B. 40° C. 60° D. 80° 5-Minute Check 6
Content Standards Preparation for G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles. Mathematical Practices 2 Reason abstractly and quantitatively. 3 Construct viable arguments and critique the reasoning of others. CCSS
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
1 2 3 4 Answer the questions using the diagram. Are 2 and 3 a linear pair? SOLUTION The angles are adjacent but their noncommon sides are not opposite rays. No.
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
Identify Angle Pairs B. ROADWAYS Name an angle pair that satisfies the condition two acute vertical angles. 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
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. UnderstandThe problem relates the measures of two supplementary angles. You know that the sum of the measures of supplementary angles is 180. Plan Draw two figures to represent the angles. Example 2
Angle Measure Solve 6x – 6 = 180 Simplify. 6x = 186 Add 6 to each side. x = 31 Divide each side by 6. Example 2
Angle Measure Use the value of x to find each angle measure. mA = x mB = 5x – 6 = 31 = 5(31) – 6 or 149 Check Add the angle measures to verify that the angles are supplementary. mA + mB = 180 31 + 149 = 180 180 = 180 Answer:mA = 31, mB = 149 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
W and Z are complementary. The measure of Z is 5 times the measure of W. Find mW SOLUTION Because the angles are complementary, mW + mZ = 90˚. ButmZ = 5( mW ), somW + 5( mW) = 90˚. Because 6(mW) = 90˚, you know that mW= 15˚.
ALGEBRA Find x and y so thatKO and HM are perpendicular. Perpendicular Lines Example 3
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
Perpendicular Lines To find y, use mMJO. mMJO = 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
Interpret Figures A. Determine whether the following statement can be justified from the figure below. Explain. mVYT = 90 Example 4
Interpret Figures B. Determine whether the following statement can be justified from the figure below. Explain. TYW andTYU are supplementary. Answer: Yes, they form a linear pair of angles. Example 4
Interpret Figures C. Determine whether the following statement can be justified from the figure below. Explain. VYW andTYS are adjacent angles. Answer: No, they do not share a common side. Example 4
A. Determine whether the statement mXAY = 90 can be assumed from the figure. A. yes B. no Example 4a
B. Determine whether the statement TAU iscomplementarytoUAY can be assumed from the figure. A. yes B. no Example 4b
C. Determine whether the statement UAX isadjacenttoUXA can be assumed from the figure. A. yes B. no Example 4c