Use the figure to name each of the following. Name a point with a capital letter. H, I, J, and K. HO. Name a segment by its endpoints. , HJ. , KI. , and OI. c. five other names for KI. , OK. , and. OI. There is one line pictured. It has several names. IK. , KO. , IO.
Name a point with a capital letter.
H, I, J, and K
Name a segment by its endpoints.
, and OI
c. five other names for KI
There is one line pictured. It has several names.
d. five different rays
The first letter names the endpoint of the ray.
, and JHIntroduction to Geometry: Points, Lines, and Planes
a. four points
b. four different segments
MP, OP, QT, ST
MQ, NR, OS
MN, NO, QR, RSIntroduction to Geometry: Points, Lines, and Planes
You are looking directly down into a wooden crate. Name each of the following.
a. four segments that intersectPT
b. three segments parallel to PT
c. four segments skew to PT
Then draw a segment that is parallel to one of the lines.Introduction to Geometry: Points, Lines, and Planes
Draw two intersecting lines. Then draw a segment that is parallel to one of the intersecting lines.
Use the lines on notebook or graph paper.
m 3 + m 4 = 180°
3 and 4 are supplementary.
m 3 + 110° = 180°
Replace m 4 with 110°.
m 3 + 110° – 110° = 180° – 110°
Solve for m 3.
m 3 = 70°Angle Relationships and Parallel Lines
Find the measure of 3 if m 4 = 110°.
1 3, 2 4, 5 7, 6 8
2 7, 6 3Angle Relationships and Parallel Lines
In the diagram, p || q. Identify each of the following.
a. congruent corresponding angles
b. congruent alternate interior angles
Classify the triangle by its sides and angles.
The triangle has no congruent sides and one obtuse angle.
The triangle is a scalene obtuse triangle.
Name the types of quadrilaterals that have at least
one pair of parallel sides.
All parallelograms and trapezoids have at least one pair of parallel sides.
Parallelograms include rectangles, rhombuses, and squares.
A contractor is framing the wooden deck shown below in the shape of a regular dodecagon (12 sides). Write a formula to find the perimeter of the deck. Evaluate the formula for a side length of 3 ft.
To write a formula, let x = the length of each side.
The perimeter of the regular dodecagon is
x + x + x + x + x + x + x + x + x + x + x + x.
Therefore a formula for the perimeter is P = 12x.
P = 12xWrite the formula.
= 12(3) Substitute 3 for x.
= 36 Simplify.
For a side length of 3 ft, the perimeter is 36 ft.
One strategy for solving this problem is to draw a diagram and count the diagonals. A nonagon has nine sides.
You can draw six diagonals from one vertex of a nonagon.
AH, AG, AF, AE, AD, and AC are some of the diagonals.Problem Solving Strategy: Draw a Diagram
How many diagonals does a nonagon have?
You can organize your results as you
count the diagonals. Do not count a
diagonal twice. (The diagonal from A to
C is the same as the one from C to A.)
Then find the sum of the numbers
Number of Diagonals
A nonagon has 27 diagonals.
X and count the diagonals. A nonagon has nine sides.
c. Find the length of WX.
TV = 300 m, WX = 300 m.
In the figure, TUV WUX.
a. Name the corresponding congruent angles.
b. Name the corresponding congruent sides.
ACB and count the diagonals. A nonagon has nine sides.
List the congruent corresponding parts of each pair of triangles. Write a congruence statement for the triangles.
MK and count the diagonals. A nonagon has nine sides.