Lesson 1-4. Angle Measure. Lesson Outline. Five-Minute Check Then & Now and Objectives Vocabulary Key Concept Examples Lesson Checkpoints Summary and Homework. Then and Now. You measure line segments (Lesson 1–2). Measure and classify angles
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Lesson 1-4 Angle Measure
Lesson Outline • Five-Minute Check • Then & Now and Objectives • Vocabulary • Key Concept • Examples • Lesson Checkpoints • Summary and Homework
Then and Now You measure line segments (Lesson 1–2) • Measure and classify angles • Identify and use congruent angles an the bisector of an angle
Objectives • Measure and classify angles • Obtuse – m > 90 • Right – m = 90 (the corner of a piece of paper) • Acute – m < 90 • Identify and use congruent angles an the bisector of an angle
Vocabulary • Degree – one three hundred and sixtieth of a circle • Ray – part of a line with one end point • Opposite rays – are collinear rays with the same end point (& form a 180 degree angle) Angle is formed by 2 noncollinear rays with a common endpoint (vertex) • Sides – composed of rays • Vertex – is the common endpoint • Interior – area between the two rays that form the angle • Exterior – area not between the two rays that form the angle
Vocabulary (cont) Special types of angles: • Right angle – measure equals 90 degrees • Acute angle – measure is less than 90 degrees • Obtuse angle – measure is greater than 90 degrees (but less than 180) • Angle Bisector – a ray that divides an angle into two congruent angles
Answer: and or are the sides of 5. Example 1 Name all angles that have B as a vertex. Answer:5, 6, 7, and ABG Name the sides of 5. Write another name for 6. Answer:EBD, FBD, DBF, and DBE are other names for 6.
Key Concept • An easy measuring device is the corner of a piece of notebook paper (or computer paper). It is a right angle.
Answer: is a right angle. Example 2a Measure TYV and classify it as right, acute, or obtuse. TYV is marked with a right angle symbol, so measuring is not necessary.
Use a protractor to find that . Answer: > is an obtuse angle. Example 2b Measure WYT and classify it as right, acute, or obtuse.
Example 2c Measure TYU and classify it as right, acute, or obtuse. Use a protractor to find that m TYU = 45° . Answer: Since 45 < 90, then TYU is an acute angle.
Example 3 INTERIOR DESIGN Wall stickers of standard shapes are often used to provide a stimulating environment for a young child’s room. A five-pointed star sticker is shown with vertices labeled. Find mGBH and mHCI if GBH HCI, mGBH = 2x + 5, and mHCI =3x – 10. Step 1 Solve for x. GBH HCI Given
Example 3 cont mGBH = mHCI Definition of congruent angles 2x + 5 = 3x – 10 Substitution 2x + 15 = 3x Add 10 to each side. 15 = x Subtract 2x from each side. Step 2 Use the value of x to find the measure of either angle. mGBH = 2x + 5Given = 2(15) + 5 Substitution, x = 15 = 30 + 5 = 35 Simplify. Answer: mGBH = 35, mHCI = 35
Summary & Homework • Summary: • Angles are named by 3 points with the vertex in the middle (or by vertex letter if no confusion) • Angles are classified as acute, right, or obtuse according to their measure • An angle bisector is a ray that divides an angle into two congruent angles (halves) • Ray is equidistance from the sides of the angle • Homework: • pg 41-3: 30-35, 39-42