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Name____________________________
Geometry Period ______
7-5 Notes
Date_______
Lesson 7-5: Discovering Angle Properties of Parallelograms
Today’s Goal: How can I discover the angle properties in quadrilaterals?
Before we explore...
FACT CHECK Consider trapezoid LMNO:
State a pair of angles that are:
1) CONSECUTIVE ANGLES _____________
2) OPPOSITE ANGLES _____________
Team Discovery Activity
We have examined the properties of parallelograms in terms of their sides and diagonals. Today we will
make some conjectures related to the interior angles of parallelograms.
Directions: Plot Parallelogram LOVE below. L( -3, 4) O(6 ,4) V(5, -2) E(-4, -2) Connect the points
with a straight edge and label all points.
Using the angles given on the
smartboard, find the degree measures of the
following angles.
Using these angle measures, answer the following questions on
the next page.
1
1)
Parallelogram Opposite Angles ConjectureDiscuss with your partners and complete the sentence below:
The opposite angles of a parallelogram (Ex: <L and <V) are ____________________.
L
O
E
Let’s say that m< L = 3x +40
V
and m< V = 9x -14
a. How can the conjecture from above help us set up an equation to solve for x?
b. Solve for x.
c. What would be the measure of angle L?
2
2)
Parallelogram Consecutive Angles ConjectureDiscuss with your partners and complete the sentence below:
The consecutive angles in a parallelogram (Ex. <L and <E) are _______________________
L
E
Let’s say that m< E = x
O
V
and m< V = x +80
a. How can the conjecture from above help us set up an equation to solve for x?
b. Solve for x.
c. What would be the measures of angle E and V?
3
Special Quadrilateral Angle Properties
The Rhombus- We know that the Rhombus is a parallelogram, so the conjectures used in
numbers 1 and 2 also apply, but the rhombus has an additional interior angle property.
Examine the following diagrams and make a conjecture about the vertex (Corner) angles to help
you complete the sentences below.
The Diagonals of a rhombus _______________________ the vertex (corner) angles.
Let’s say that m< DCA = 25 and the measure of < BCA = 2x -5.
a. What is the value of x?
b. What is the measure of < CDA?
4
The Trapezoid- The trapezoid also has some interesting interior angle relationships. Examine
the diagrams below:
a. What relationship do you notice between the consecutive angles
located between the bases?
b. In trapezoids, the bases are parallel. What type of special angle
pair are angles <BAD and <CDA? (Consider AD a transversal).
BASE
Why does this explain what you wrote in part a?
Application: Solve for x and find the measure of <A and <D.
Let’s Practice! Work with your teammates
on the following
questions based on the properties you
discovered today.
1) Find x and y so
that the quadrilateral is a parallelogram.
2) ABCD is a rhombus.
a.
If m∠CBD = 58, find m∠ACB.
b. If m∠BAD = 100 , find m∠BCD.
3) Given Isosceles Trapezoid ABCD, find the m< D
4)
Find the m<L