Download Lesson 7-8a

7-8
6th grade math
Quadrilaterals
Objective
• To classify and draw quadrilaterals. Find
missing angles in quadrilaterals.
• Why? To further your knowledge in
measurement and geometry and keeping
building a strong foundation in MG in HS
California State Standards
MG 2.3: Draw quadrilaterals … from information
about them (e.g., quadrilateral having equal
sides but no right angles, …).
AF 1.1 : Write and solve one-step linear
equations with one variable.
AF 3.2: Express in symbolic form simple
relationships arising from geometry.
MG 2.0: Identify and describe the properties of
two-dimensional figures.
MR 2.2: Apply strategies and results from simpler
problems to more complex problems.
• Quadrilateral
Vocabulary
– A polygon with 4 sides. Sum of all 4 angles = 360°
• Diagonal
– A segment that joins two vertices (plural of vertex)
of a polygon, but is not a side. A diagonal divides a
quadrilateral into two triangles.
• Trapezoid
Vocabulary
– A quadrilateral with only one pair of opposite sides
parallel
or
• Parallelogram
– A quadrilateral with each pair of opposite sides
parallel and congruent. A rectangle with no right
angles.
• Rhombus
– A parallelogram with all sides congruent. A square
with no right angles.
Vocabulary
• Rectangle
– A parallelogram with 4 right angles. 2 pairs of
congruent sides.
• Square
– A parallelogram with all sides congruent and 4 right
angles.
How to Find Missing Angles in Quadrilaterals
1) Add the 3 known angles
2) Subtract 360 from Step 1
3) Check work
Quadrilateral with 3 known
angles: 90° + 90° + 115°
360° - (90° + 90° + 115°)
= 360° - 295 = 65°
How to Find Missing Angles in Quadrilaterals
Find the missing angle measures in
quadrilateral JKLM.
K
L
s
J
┐
r
u
M
150°
t
┌45° N
To solve take apart slowly. Look for
adjacent, vertical, complementary,
supplementary angles
A) m∠r =
m∠r is supplementary to ∠L (150°)
m∠r = 180 – 150 = 30°
B) m∠t =
m∠t is ½ of ∠N
m∠t = 45°
C) m∠u=
m∠u is part of ∠r and 45°
180 – (30 + 45)
m∠u= = 105°
D) m∠s=
m∠s is part of quadrilateral
sJ150°t
= 360 – (s + 90 + 150 + 45)
m∠s = 75°
Try It!
Find the missing angle n and classify
the polygon.
1)
1) 90°, rectangle (all angles
add to 360)
2) 70°, parallelogram (all
angles add to 360 and vertical
angles are equal)
2)
3) 110°, trapezoid (all angles
3)
4)
add to 360 and opposite angles are
equal)
4) 40°, quadrilateral (all
angles add to 360)
Objective Review
• To classify and draw
quadrilaterals. Find missing
angles in quadrilaterals.
• Why? To You now have furthered your
knowledge in measurement and geometry and
keeping building a strong foundation in MG in
HS
• Quadrilaterals are classified according to the
special properties of their sides and angles.
• Knowing the properties for complementary and
supplementary angles, and the sums of the
angle measures of triangles and quadrilaterals
can help you find the measure of an unknown
angle.
Independent Practice
• Complete problems 616
• Copy original problem
first.
• Show all work!
• If time, complete Mixed
Review: 17-22
• If still more time, work
on Accelerated Math.