Holt Geometry 1-1 Understanding Points, Lines, and Planes 1-1 Unit 1 – Introduction and Construction Holt Geometry Lesson Presentation Lesson Presentation Homework

Holt Geometry 1-1 Understanding Points, Lines, and Planes Identify, name, and draw segments, lines, angles, bisected angles, bisected segments, parallel and perpendicular lines. Make geometric constructions of these terms. Objectives Unit 1 – Introduction and Construction

Holt Geometry 1-1 Understanding Points, Lines, and Planes Key Vocabulary Activity- Create a flipbook using the following terms: segment angle line construction bisected angle bisected segment parallel lines perpendicular lines Unit 1 – Introduction and Construction

Holt Geometry 1-1 Understanding Points, Lines, and Planes Unit 1 – Introduction and Construction

Holt Geometry 1-1 Understanding Points, Lines, and Planes Unit 1 – Introduction and Construction

Holt Geometry 1-1 Understanding Points, Lines, and Planes Example 1: Drawing Segments and Rays Draw and label each of the following. A. a segment with endpoints M and N. B. a line with a points S and T. M N S T Unit 1 – Introduction and Construction

Holt Geometry 1-1 Understanding Points, Lines, and Planes Draw and label a ray with endpoint M that contains N. Check It Out! Example 1 MN Unit 1 – Introduction and Construction

Holt Geometry 1-1 Understanding Points, Lines, and Planes Example 2: Representing Intersections A. Sketch two lines intersecting in exactly one point. Unit 1 – Introduction and Construction

Holt Geometry 1-1 Understanding Points, Lines, and Planes Congruent segments are segments that have the same length. In the diagram, PQ = RS, so you can write PQ  RS. This is read as “segment PQ is congruent to segment RS.” Tick marks are used in a figure to show congruent segments. Unit 1 – Introduction and Construction

Holt Geometry 1-1 Understanding Points, Lines, and Planes You can make a sketch or measure and draw a segment. These may not be exact. A construction is a way of creating a figure that is more precise. One way to make a geometric construction is to use a compass and straightedge. Unit 1 – Introduction and Construction

Holt Geometry 1-1 Understanding Points, Lines, and Planes Example 3: Copying a Segment Sketch, draw, and construct a segment congruent to MN. Step 1 Estimate and sketch. Estimate the length of MN and sketch PQ approximately the same length. PQ Unit 1 – Introduction and Construction

Holt Geometry 1-1 Understanding Points, Lines, and Planes Example 3 Continued Sketch, draw, and construct a segment congruent to MN. Step 2 Measure and draw. Use a ruler to measure MN. MN appears to be 3.5 in. Use a ruler to draw XY to have length 3.5 in. XY Unit 1 – Introduction and Construction

Holt Geometry 1-1 Understanding Points, Lines, and Planes Example 3 Continued Sketch, draw, and construct a segment congruent to MN. Step 3 Construct and compare. Use a compass and straightedge to construct ST congruent to MN. A ruler shows that PQ and XY are approximately the same length as MN, but ST is precisely the same length. Unit 1 – Introduction and Construction

Holt Geometry 1-1 Understanding Points, Lines, and Planes The midpoint M of AB is the point that bisects, or divides, the segment into two congruent segments. If M is the midpoint of AB, then AM = MB. So if AB = 6, then AM = 3 and MB = 3. An angle is a figure formed by two rays, or sides, with a common endpoint called the vertex (plural: vertices). You can name an angle several ways: by its vertex, by a point on each ray and the vertex, or by a number. Unit 1 – Introduction and Construction

Holt Geometry 1-1 Understanding Points, Lines, and Planes Angle Name R, SRT, TRS, or 1 You cannot name an angle just by its vertex if the point is the vertex of more than one angle. In this case, you must use all three points to name the angle, and the middle point is always the vertex. Unit 1 – Introduction and Construction

Holt Geometry 1-1 Understanding Points, Lines, and Planes Example 4 Write the different ways you can name the angles in the diagram. RTQ, T, STR, 1, 2 Unit 1 – Introduction and Construction

Holt Geometry 1-1 Understanding Points, Lines, and Planes The measure of an angle is usually given in degrees. Since there are 360° in a circle, one degree is of a circle. When you use a protractor to measure angles, you are applying the following postulate. Unit 1 – Introduction and Construction

Holt Geometry 1-1 Understanding Points, Lines, and Planes The measure of an angle is the absolute value of the difference of the real numbers that the rays correspond with on a protractor. If OC corresponds with c and OD corresponds with d, mDOC = |d – c| or |c – d|. Unit 1 – Introduction and Construction

Holt Geometry 1-1 Understanding Points, Lines, and Planes Find the measure of each angle. Example 5: Measuring Angles A. WXV B. ZXW mWXV = 30° mZXW = |130° - 30°| = 100° Unit 1 – Introduction and Construction

Holt Geometry 1-1 Understanding Points, Lines, and Planes Check It Out! Example 5 Use the diagram to find the measure of each angle. a. BOA b. DOB c. EOC mBOA = 40° mDOB = 125° mEOC = 105° Unit 1 – Introduction and Construction

Holt Geometry 1-1 Understanding Points, Lines, and Planes Congruent angles are angles that have the same measure. In the diagram, mABC = mDEF, so you can write ABC  DEF. This is read as “angle ABC is congruent to angle DEF.” Arc marks are used to show that the two angles are congruent. Unit 1 – Introduction and Construction

Holt Geometry 1-1 Understanding Points, Lines, and Planes An angle bisector is a ray that divides an angle into two congruent angles. JK bisects LJM; thus LJK  KJM. Unit 1 – Introduction and Construction

Holt Geometry 1-1 Understanding Points, Lines, and Planes Unit 1 – Introduction and Construction

Holt Geometry 1-1 Understanding Points, Lines, and Planes Example 6: Identifying Types of Lines Identify each of the following. A. a pair of parallel segments LM ||QR NS  SP B. a pair of perpendicular segments Unit 1 – Introduction and Construction

Holt Geometry 1-1 Understanding Points, Lines, and Planes Check It Out! Example 6 Identify each of the following. a. a pair of parallel segments b. a pair of perpendicular segments BF || EJ BF  FJ Unit 1 – Introduction and Construction

Holt Geometry 1-1 Understanding Points, Lines, and Planes The perpendicular bisector of a segment is a line perpendicular to a segment at the segment’s midpoint. HYPOTHESISCONCLUSION Unit 1 – Introduction and Construction

Holt Geometry 1-1 Understanding Points, Lines, and Planes Unit 1 – Introduction and Construction Label and draw each of the following: a segment, a line, an angle, bisected angles, bisected segments, parallel and perpendicular lines. Ticket out the door:

Holt Geometry 1-1 Understanding Points, Lines, and Planes Homework Unit 1 – Introduction and Construction Angles Segments Bisect Parallel Lines Perpendicular Lines Identify and describe each of these terms in your daily life: