lesson 4 menu five-minute check (over lesson 10-3) main ideas and vocabulary targeted teks key...
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Five-Minute Check (over Lesson 10-3)
Main Ideas and Vocabulary
Targeted TEKS
Key Concept: The Pythagorean Theorem
Example 1: Find the Length of the Hypotenuse
Example 2: Find the Length of a Side
Example 3: Pythagorean Triples
Key Concept: Converse of the Pythagorean Theorem
Example 4: Check for Right Triangles
• hypotenuse
• legs
• Pythagorean triple
• converse
• Solve problems by using the Pythagorean Theorem.
• Determine whether a triangle is a right triangle.
Find the Length of the Hypotenuse
Find the length of the hypotenuse of a right triangle if a = 18 and b = 24.
c2 = a2 + b2 Pythagorean Theorem
c2 = 182 + 242 a = 18 and b = 24
c2 = 900 Simplify.
Answer: The length of the hypotenuse is 30 units.
Take the square root of each side.
Use the positive value.
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 45 units
B. 85 units
C. 65 units
D. 925 units
Find the length of the hypotenuse of a right triangle if a = 25 and b = 60.
Find the Length of a Side
Find the length of the missing side. If necessary, round to the nearest hundredth.
c2 = a2 + b2 Pythagorean Theorem
162 = 92 + b2 a = 9 and c = 16
256 = 81 + b2 Evaluate squares.
175 = b2 Subtract 81 from each side.
Answer: about 13.23 units
Use the positive value.
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. about 12 units
B. about 22 units
C. about 16.25 units
D. about 5 units
Find the length of the missing side.
STANDARDIZED TEST PRACTICE What is the area of triangle XYZ?
A 94 units2
B 128 units2 C 294 units2 D 588 units2
Pythagorean Triples
Read the Test Item
Solve the Test Item
Step 1 Check to see if the measurements of this triangle are a multiple of a common Pythagorean triple. The hypotenuse is 7 ● 5 units and the leg is 7 ● 4 units. This triangle is a multiple of a (3, 4, 5) triangle.
7 ● 3 = 21
7 ● 4 = 28
7 ● 5 = 35
The height of the triangle is 21 units.
Pythagorean Triples
Step 2 Find the area of the triangle.
Answer: The area of the triangle is 294 square units.Choice C is correct.
Pythagorean Triples
Area of a triangle
b = 28 and h = 21
Simplify.
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 764 units2
B. 480 units2
C. 420 units2
D. 384 units2
STANDARDIZED TEST PRACTICE What is the area of triangle RST?
A. Determine whether the side measures of 7, 12, 15 form a right triangle.
Since the measure of the longest side is 15, let c = 15, a = 7, and b = 12. Then determine whether c2 = a2 + b2.
Answer: Since c2 ≠ a2 + b2, the triangle is not a right triangle.
Check for Right Triangles
225 = 49 + 144 Multiply.?
?152 = 72 + 122 a = 7, b = 12, and c = 15
225 ≠ 193 Add.
c2 = a2 + b2 Pythagorean Theorem
B. Determine whether the side measures of 27, 36, 45 form a right triangle.
Check for Right Triangles
Since the measure of the longest side is 45, let c = 45, a = 27, and b = 36. Then determine whether c2 = a2 + b2.
Answer: Since c2 = a2 + b2, the triangle is a right triangle.
c2 = a2 + b2
Pythagorean Theorem
452 = 272 + 362 a = 27, b = 36, and c = 45
2025 = 729 + 1296Multiply.
2025 = 2025 Add.
1. A
2. B
3. C
0%0%0%
A B C
A. right triangle
B. not a right triangle
C. cannot be determined
A. Determine whether the following side measures form right triangles: 33, 44, 55.
1. A
2. B
3. C
0%0%0%
A B C
A. right triangle
B. not a right triangle
C. cannot be determined
B. Determine whether the following side measures form right triangles: 15, 12, 24.