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TODAY IN GEOMETRY…Practice: Solving missing sides using the
Pythagorean Theorem
Learning Target 1: Use the Converse of the Pythagorean Theorem determine if a triangle is a right triangle
Independent Practice
Learning Target 2: Use the properties of Special Right Triangles to find missing sides.
REVIEW:
USING THE PYTHAGOREAN THEOREM TO FIND MISSING
SIDES
𝑥58
26
PRACTICE: Identify the unknown side as a leg or hypotenuse. Then, find the unknown side length of the right triangle. Write your answer in the simplest radical form.
The unknown side is attached to the right angle so it is a leg of the triangle.
Use the Pythagorean theorem to find the missing leg:
6
8
12
𝑥
PRACTICE: Identify the unknown side as a leg or hypotenuse. Then, find the unknown side length of the right triangle. Write your answer in the simplest radical form.
The unknown side is not attached to the right angle so it is a hypotenuse of the triangle.(There are two right triangles. You must find a before you can find x.)Use the Pythagorean theorem to find a:
𝑎
Use the Pythagorean theorem again to find x:
¿10
CONVERSE TO THE PYTHAGOREAN THEOREM:
3 PARTS!!!
PART 1:
RIGHT TRIANGLE if…
𝑎2+𝑏2=𝑐2
PART 2:
ACUTE TRIANGLE if…
PART 3:
OBTUSE TRIANGLE if…
𝑎2+𝑏2>𝑐2𝑎2+𝑏2<𝑐2
CONVERSE TO THE PYTHAGOREAN THEOREM: 𝑎 𝑐
𝑏
𝐵
𝐴𝐶
8
4 43
PRACTICE: Tell whether a triangle with the given side lengths is a right triangle. Assign the given lengths to the sides of
the triangle. The largest side is always assigned the hypotenuse!
Use the Pythagorean theorem to check if it is a right triangle.
? ? ? NOT A RIGHT ANGLE!
TRIANGLE IS OBTUSE!
4 ,43 ,8
4 8
43
11
10 14
PRACTICE: Tell whether a triangle with the given side lengths is a right triangle. Assign the given lengths to the sides of
the triangle. The largest side is always assigned the hypotenuse!
Use the Pythagorean theorem to check if it is a right triangle.
? ? ? NOT A RIGHT ANGLE!
TRIANGLE IS ACUTE!
10 ,11 ,14
10 11
14
5.2
4.3 6.1
PRACTICE: What kind of triangle (acute, obtuse or right) can be formed with segment lengths
Assign the given lengths to the sides of the triangle. The largest side is always assigned the hypotenuse!
Use the Pythagorean theorem to check if it is a right triangle.
? ? ? NOT A RIGHT ANGLE!
TRIANGLE IS ACUTE!
4.3 5.2
6.1
PRACTICE: Graph points . Connect the points to form . Decide whether the triangle is acute, right or obtuse.
𝐴 (−2 ,4 )𝐵 (6 ,0 )𝐶 (−5 ,−2)
𝑨
𝑩
𝑪
Use the distance formula to find the segment lengths:
Use the Pythagorean theorem to check if it is a right triangle.
? ? ? IT IS A RIGHT TRIANGLE!
HOMEWORK #2:
Pg. 444:1-6, 8, 10, 12
If finished, work on other assignments:
HW #1: Pg. 436: 3-29 odd
SPECIAL RIGHT TRIANGLES:
:
√𝟐 𝒙𝒙
45 °
45 °𝒙
𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆=𝒍𝒆𝒈 ·√𝟐Example:
𝑥
8PRACTICE: Find the value of x. Write your answer in simplest radical form.
Substitute known values
8
𝑥¿8∙√2
8 √2=¿
3√2 𝑥
PRACTICE: Find the value of x. Write your answer in the simplest radical form.
3√2
Substitute known values Multiply square roots
Simplify
¿6
𝑥 3√2∙√2¿
Substitute known values
Divide by Simplify
√2𝑥∙
𝑥 9√2
PRACTICE: Find the value of x. Write your answer in the simplest radical form.
𝑥
9√2¿
¿9
9=¿
10 𝑥
PRACTICE: Find the value of x. Write your answer in simplest radical form.
Substitute known values
Divide by
𝑥¿5√2
¿5√2
10 𝑥∙√2¿
Rationalize the denominator
:
𝟐 𝒙𝒙
60 °
30 °√𝟑 𝒙
EX: ¿2 𝑥
EX: ¿√3 𝑥
4𝑥
PRACTICE: Find the value of x and y. Write your answer in simplest radical form.
30 °
60 °
𝑦
Substitute known values
Multiply
Substitute known values
Simplify
8=¿
¿ 4√3*We’re given the shorter leg first, we can start with any of the two equations for 30-60-90 triangles!
2𝑥 ∙4¿
4𝑦 ∙√3¿
20
𝑥
PRACTICE: Find the value of x and y. Write your answer in simplest radical form.
30 °
60 °
𝑦
Substitute values
Divide Simplify
Substitute values
*We’re given the hypotenuse first, we can start with the first equation for 30-60-90 triangles!
220 ∙𝑥¿
10𝑦 ∙√3¿¿10
¿10√3
√3 𝑥
PRACTICE: Find the value of x and y. Write your answer in simplest radical form.
30 °
60 °
𝑦 Substitute known values
Multiply
Substitute known values
Multiply Simplify
¿2√3
¿3
2𝑥 ∙√3¿
√3𝑦 ∙√3¿
*We’re given the shorter leg first, we can start with any of the two equations for 30-60-90 triangles!
HOMEWORK #3:
Pg. 461: 3-18
If finished, work on other assignments:
HW #1: Pg. 436: 3-29 oddHW #2: Pg. 444; 1-6, 8, 10, 12
