Download Name: ____________ TP: ____ CRS Geometry Content/PPF601

CW#54H: Special Right Triangles: 45 – 45 – 90
Honors Geometry
Name: __________________________________________ TP: ____
CRS
Objective
Geometry Content/PPF601 - Apply properties of 30-60-90, 45-45-90, similar, and congruent triangles
Critical
Thinking
Reasoning and Argumentation: Construct well-reasoned arguments or proofs to explain issues; Address challenges
by providing a logical explanation or refutation, or by acknowledging the accuracy of the challenge


9.7 Describe the relationship between sides of a 45-45-90 triangle
9.8 Find the missing side length in a 45-45-90 triangle (A.K.A “isosceles right triangle”)
Guided Practice Problems:
1) Find the length of the
hypotenuse.
2) Find x.
3) Find the missing side
length.
3x+3
12√2
Independent Practice:
4) Find x.
5) Find x.
6. Area. The diagonal of a square is 12 inches.
Find the area of the base triangle.
7. Find x.
8. Baseball. Using the diagram below, find the
distance from home plate to second base.
Round to the nearest whole number.
9. Fill in the table.
X
5
Y
PUSH IT TO THE LIMIT.
2
4
2
9
24
Challenge Problems:
10) Squares. The area of the shaded region is 45
inches squared. Find the missing hypotenuses for
both triangles. Write a proof explaining how you
found your answer.
11) Eric wishes to paint the image below on front of
Ms. Ziegler’s door. She said ok, as long as 75% of
the door remains unpainted. Given the following
information, will Eric be permitted to paint his
masterpiece and if so how many copies will fit on
the door?
3 in
7 in
6ft
5 in
7√2 in.
r = 3 in
r = 1.5 in
12) You make a guitar pick that resembles an
equilateral triangle with side lengths of 32
millimeters. What is h? (Assume BD is a | bisector
of AC) Write a Proof.
4ft
Be careful not to include the doorknob in your area
calculation of the door. Likewise, the cut out circle in
Eric’s painting.
Brain Teaser:
You have two buckets - one holds exactly 5 gallons and the other
3 gallons
How can you measure out 4 gallons of water into the 5 gallon
bucket ?
(Assume that you have an unlimited supply of water and that there
are no measurement markings of any kind on the buckets.)
Answer and Prove the following:
a. What type of triangle is ∆ABC, ∆BDC?
b. Compare your derived side lengths and
make a general rule that describes the
hypotenuse to leg relationship for ∆BDC.
(Use the 45-45-90 theorem as a guide.)
THINK RATIOS!
PUSH IT TO THE LIMIT.