WARM UP
• Systems of Equations. Solve by substitution!
1.
𝑦 =𝑥+5
𝑦 + 3𝑥 = 25
2.
−5𝑥 + 4𝑦 = 20
10𝑥 − 8𝑦 = −40
WARM UP
• Systems of Equations. Solve by substitution!
1.
(5, 10)
𝑦 =𝑥+5
𝑦 + 3𝑥 = 25
2.
−5𝑥 + 4𝑦 = 20
10𝑥 − 8𝑦 = −40
Infinitely many solutions
Snap Wink
O 1. Stand up.
O 2. Wink your left eye and snap your right
hand index finger and thumb at the same
time.
O 3. Wink your right eye and snap your left
hand index finger and thumb at the same
time.
O 4. Switch back and forth as fast as you can.
Chapter 1
Honors Geometry
1-1 Points, Lines and Planes
• Collinear Points: Points that lie on the same
line.
• Coplanar Points: points that lie on the same
plane.
Example 1A: Use the figure to name a line containing
point K
Example 1A: Use the figure to name a line containing
point K
Answer: The line can be named as line a.
There are three points on the line. Any two of the points can
be used to name the line
For example:
Example 1B: Use the figure to name a plane
containing point L
Example 1B: Use the figure to name a plane
containing point L
Answer: The plane can be named as plane B
• You can also use any three NONCOLLINEAR
points to name the plane.
For example: plane JKM plane KLM plane JLM
• The letters of each of these names can be
reordered to create other acceptable names
for this plane. For example, JKM can also be
written as JMK, MKJ, KJM, KMJ, and MJK.
There are 15 different three-letter names for
this plane.
Example 2A: Name the geometric
shape modeled by a 10 x 12 patio.
Example 2A: Name the geometric
shape modeled by a 10 x 12 patio.
• Answer: The patio models a plane
Example 3: Name the geometric
shape modeled by a button on a table
Example 3: Name the geometric
shape modeled by a button on a table
• Answer: The button on the table models a
point on a plane.
• Two or more geometric figures intersect if
they have one or more points in common
• The intersection of the figures is the set of
points the figures have in common.
Example 4
• Draw and label a figure for the following
situation: Plane R contains lines AB and DE,
which intersect at point P. Add point C on
plane R so that it is not collinear with line AB
or line DE.
Draw a surface to represent plane R and label it.
Your plane should look something like
this:
Example 5:
• Draw and label a figure for the following
situation. Line QR on a coordinate plane
contains Q(-2, 4) and R(4, -4). Add point T so
that T is collinear with these points
Example 5:
• Draw and label a figure for the following
situation. Line QR on a coordinate plane
contains Q(-2, 4) and R(4, -4). Add point T so
that T is collinear with these points
Example 6
• A: How many planes appear in this figure?
Example 6
• A: How many planes appear in this figure?
• There are 2 planes,
plane S and plane ABC
Example 6
• B: Name three points that are collinear.
Example 6
• B: Name three points that are collinear.
• Answer: Points A, B, and
D are collinear
Example 6
• C. Are points A, B, C, and D coplanar? Explain.
Example 6
• C. Are points A, B, C, and D coplanar? Explain.
• Answer: Points A, B, C,
and D all lie in plane ABC,
so they are coplanar.
Example 6
• D: At what point do lines DB and CA intersect?
Example 6
• D: At what point do lines DB and CA intersect?
• The two lines intersect
at point A.