Download Joe uses metal rods to make triangular frameworks in

Common Core 7
Unit 7: Applications of Geometric Problems
Mrs. Melott*, Mr. Herman, Mr. Rocco
7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given
conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the
conditions determine a unique triangle, more than one triangle, or no triangle.
Page
This packet belongs to ___________________________________
1
7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step
problem to write and solve simple equations for an unknown angle in a figure.
SWBAT: _____________________________________________________________________________________
7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given
conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the
conditions determine a unique triangle, more than one triangle, or no triangle.
DETAILS: Students draw geometric shapes with given parameters. Parameters could include parallel
lines, angles, perpendicular lines, line segments, etc.
Example 1:
Draw a quadrilateral with one set of parallel sides and no right angles.
Page
2
Students understand the characteristics of angles and side lengths that create a unique triangle, more than
one triangle or no triangle.
Example 2:
Can a triangle have more than one obtuse angle? Explain your reasoning.
Example 3:
Will three sides of any length create a triangle? Explain how you know which will work.
Possibilities to examine are:
a. 13 cm, 5 cm, and 6 cm
b. 3 cm, 3cm, and 3 cm
Page
3
c. 2 cm, 7 cm, 6 cm
Example 4:
Is it possible to draw a triangle with a 90˚ angle and one leg that is 4 inches long and one leg that is 3
inches long? If so, draw one. Is there more than one such triangle?
(NOTE: Pythagorean Theorem is NOT expected – this is an exploration activity only)
Example 5:
Page
4
Draw a triangle with angles that are 60 degrees. Is this a unique triangle? Why or why not?
Example 6:
Here’s an example of an isosceles triangle with only one 80°angle.
Is this the only possibility or can another triangle be drawn that will meet these conditions?
*Students recognize that the sum of the angles of any triangle will be ________.
Page
5
*Students understand that the angles of any quadrilateral will sum to _________.
Base angles of an isosceles triangle are equal

Angle and side length relationships between scalene, isosceles, and equilateral triangles

Angle and side length relationships between obtuse, acute and right triangles
Page

6
Other explorations to consider:
In the space below, draw an acute scalene triangle.
In the space below, draw a right isosceles triangle.
In the space below, draw an acute scalene triangle.
Page
7
In the space below, draw an obtuse scalene triangle.
Emma Watson dares Wiz Khalifa to draw a right equilateral triangle. After many hours of trying, Wiz
Khalifa calls you and says, "I can't seem to figure it out, but I'm sure that if I keep drawing triangles
I'll find one." What is the best geometrical advice that you can give to Wiz Khalifa? Explain.
Page
8
Andrew Luck dares Jennifer Lawrence to draw an obtuse equilateral triangle. After many hours of
trying, Jennifer Lawrence calls you and says, "I can't seem to figure it out, but I'm sure that if I keep
drawing triangles I'll find one." What is the best geometrical advice that you can give to Jennifer
Lawrence? Explain.
Joe uses metal rods to make triangular frameworks in which each side has a different length.
He buys metal rods which have lengths 1 meter, 2 meters, 3 meters, etc. and he always keeps one
rod of each length in stock.
This diagram shows one of Joe’s triangular frameworks.
a, b, c are all integers and c > b > a.
That is, c is the longest side, a is the shortest side and a, b, c are whole numbers.
(a) How many different triangular frameworks can Joe make which have a longest side 7 meters
long, using the rods he has in stock? Show your work.
(b) Investigate this situation for other values of c.
Page
9
(c) Write down any generalizations you can make.
Michael Vick is tutoring Rihanna in math. Michael Vick says that sides AB and BC in the triangle
below are congruent. "That's crazy!" says Rihanna. "Here, I'll show you," says Michael Vick.
(a) "Draw a line from B to AC that intersects AC at a right angle, and label the point of intersection
D."
(b) "What do you know about the angles DBA and DBC? Explain.
(c) "What do you know about triangles ADB and CDB? Explain.
Page
10
(d) "What do you know about sides BA and BC? Explain.
Wiz Khalifa is tutoring Alicia Keys in math. Wiz Khalifa says that ∠A and ∠C in the triangle below
are congruent. "That's crazy!" says Alicia Keys. "Here, I'll show you," says Wiz Khalifa.
(a) "Draw the midpoint of AC and label it D, and draw a line from D to B."
(b) "What do you know about AD and DC? Explain.
(c) "What do you know about triangles ADB and CDB? Explain.
(d) "What do you know about the interior angles of triangles ADB and CDB? Explain.
Page
11
(e) "What do you know about ∠A and ∠C ?
SWBAT: _____________________________________________________________________________________
7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step
problem to write and solve simple equations for an unknown angle in a figure.
Page
12
DETAILS: Students use understandings of angles and deductive reasoning to write and solve equations
Page
13
NOTES:
Page
14
Page
15
Page
16
Example1:
Write and solve an equation to find the measure of angle x.
Example 2:
Page
17
Find the measure of angle x.
Example 3:
Find the measure of angle b.
Note: Not drawn to scale.
Page
18
The angles below are complementary. Find the value of x
Find all missing angles. You can't find angles that touch borders.
Page
19
m∠A=84 ∘ and m∠B=68 ∘ . Are the angles complementary?
Find all the missing angles. You can't find angles that touch borders. For a challenge, find the hidden
angle.
Page
20
∠TMW and ∠WMF are complementary and congruent. What is the measure of ∠TMW ?
The angles below are supplementary. Find the value of x
The angles below are supplementary. Find the value of x
Page
21
The angles below are supplementary. Find the value of x
Page
22
Find all missing angles. You can't find angles that touch borders.
Find all the missing angles. You can't find angles that touch borders. For a challenge, find the hidden
angle.
Page
23
m∠A=116 degrees and m∠B=52 degrees. Are the angles supplementary?
The angles below are supplementary. What is the value of the missing angle?
Page
24
Find all missing angles. You can't find angles that touch borders.
Page
25
Find all the missing angles. You can't find angles that touch borders. For a challenge, find the hidden
angle.
Three identical white shapes and three identical grey shapes are fitted together to make this pattern.
How big is the angle marked n degrees? (Drawing not to scale)
Here is a design for a tile in the shape of a regular octagon.
The design is made from eight squares all the same size placed symmetrically round the octagon.
(a) Join eight points in the diagram to make another regular octagon.
Page
26
(b) The inner sides of the squares form a ‘star’ in center of the tile. How many sides does the star
have?
(c) Draw in all the lines of symmetry of the star.
How many lines of symmetry does the star have?
What is the angle between each line of symmetry and the next? Explain how you know.
(d)
Explain why angle B is 45
∘
27
∘
Page
Angle A is 135
Imagine that you are an archaeologist, and you have just uncovered this old Roman floor mosaic in
Spain.
Page
28
You telephone your office in New York to tell them about the exciting discovery. Describe the
complete pattern (shown above) as precisely as you can, so someone else can draw it without
seeing it. Try to describe the shapes, the symmetry and the angles.
Symmetry
SWBAT:_____________________________________________________________
What does symmetry mean when we look at people?
2 sides are mirror images:____________________
The line that cuts the image into 2 identical pieces: ______________________
When you turn the object so that it looks exactly the same; the number of positions in which it looks
exactly the same gives you its order of symmetry: __________________
Select from the following terms:
line of symmetry
29
line symmetry
Page
Rotational symmetry
0
/common-core-st
...
5
w ord_docx
30
no
Page
0
0
Page
31