Download 1.2/3 Measuring and Constructing Segments and Angles

1.2/3 Measuring and Constructing Segments and Angles
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Coordinate: a number used to identify the location of a point
Distance: absolute value of the difference of the coordinates of any two points
Length: distance between two points
Example 1: Find each length
A) BC
B) AC
Congruent Segments: segments that have the same length
Construction: a way of creating a figure that is considered to be mathematically precise
*uses a compass and straightedge, Geometry software, or paper folding
Between: given 3 points A, B, and C, B is between A and C if and only if all three of the points lie
on the same line and AB + BC = AC
Example 2:
A) G is between F and H, FG = 6 and FH = 11. Find GH.
B) M is between N and O. Find NO.
Midpoint: point that divides a segment into two congruent segments
Bisect: to divide into two congruent parts.
Example 3: The map shows the route for a race. You are at X, 6000 ft from the first
checkpoint C. The second checkpoint D is located at the midpoint between C and the end
of the race Y. The total race is 3 miles. How far apart are the 2 checkpoints?
Segment Bisector: any ray, segment, or line that intersects a segment at its midpoint
Example 4: D is the midpoint of EF. ED = 4x + 6 and DF = 7x – 9. Find ED, DF, and EF.
Angle: a figure formed by 2 rays with a common endpoint
Vertex: the common endpoint of the sides of the angle
Interior of an Angle: set of all points between the sides of the angle
Exterior of an Angle: set of all points outside the angle
Example 5: A surveyor recorded the angles formed by a transit (Point A) and three distant
points B, C, and D. Name three of the angles.
Measure of an Angle: angles are measured in degrees
Degree: unit of angle measure
Example 6: Find the measure of each angle. Then classify each as acute, right, or obtuse.
A) 𝑚∠𝑊𝑋𝑉
B) 𝑚∠𝑍𝑋𝑊
Congruent Angles: angles that have the same measure
Example 7: 𝒎∠𝑫𝑬𝑮 = 𝟏𝟏𝟓, and 𝒎∠𝑫𝑬𝑭 = 𝟒𝟖. Find 𝒎∠𝑭𝑬𝑮
Angle Bisector: ray that divides an angle into two congruent angles
⃗⃗⃗⃗⃗⃗⃗ bisects ∠𝑱𝑲𝑳, 𝒎∠𝑱𝑲𝑴 = (𝟒𝒙 + 𝟔), and 𝒎∠𝑴𝑲𝑳 = (𝟕𝒙 − 𝟏𝟐). Find
Example 8: 𝑲𝑴
𝒎∠𝑱𝑲𝑴
Homework p17 #12-32 even, 47-49 & p25 #12-32 even, 46, 52, 58