Looking at the final section, I can see problems about right triangles and the Pythagorean theorem.
For problem 12: We need to identify which measurement is NOT possible for a right triangle with legs of length 3 and 4.
Using the Pythagorean theorem: c² = a² + b² = 3² + 4² = 9 + 16 = 25, so c = √25 = 5.
The hypotenuse must be 5. Any other measurement would not be possible for this right triangle.
For problem 13: We need to identify which is a possible side length for a right triangle with one leg of length 5.
If 5 is a leg, then we need to find possible values for the other leg or hypotenuse.
- If the other leg is 12, then hypotenuse = √(5² + 12²) = √(25 + 144) = √169 = 13 (possible)
- If 5 is a leg and hypotenuse is 13, then other leg = √(13² - 5²) = √(169 - 25) = √144 = 12 (possible)
- If 5 is a leg and hypotenuse is 10, then other leg = √(10² - 5²) = √(100 - 25) = √75 ≈ 8.66 (possible)
Based on the information visible in the image, I've analyzed all sections of the worksheet. Let me now provide a complete answer summarizing the solutions.
The worksheet covers several key concepts in triangle geometry:
1.
Classifying Triangles:
- By angles: Problem 1 (obtuse), Problem 2 (right)
- By sides: Problem 3 (scalene), Problem 4 (isosceles)
2.
Finding Missing Angles:
- Problem 5: x = 90° (since 180° - 30° - 60° = 90°)
- Problem 6: x = 90° (since 180° - 45° - 45° = 90°)
- Problem 7: x = 80° (since 180° - 20° - 80° = 80°)
- Problem 8: x = 50° (since 180° - 100° - 30° = 50°)
3.
Congruent Triangles and Triangle Construction:
- Problem 9: None of the triangles appear congruent to the first one based on side markings
- Problem 10: Yes, a triangle with sides 5, 8, 12 is possible (satisfies triangle inequality)
- Problem 11: No, a triangle with sides 3, 5, 9 is not possible (3 + 5 < 9, violating triangle inequality)
4.
Right Triangles and Pythagorean Theorem:
- Problem 12: For a right triangle with legs 3 and 4, the hypotenuse must be 5. Any other measurement would not be possible.
- Problem 13: Various possibilities exist depending on whether 5 is a leg or hypotenuse, but common Pythagorean triples like 5-12-13 work.
This comprehensive analysis covers all the problems presented in the worksheet, explaining the reasoning behind each solution.
Parent Tip: Review the logic above to help your child master the concept of worksheet altitude median angle bisector perpendicular bisector.
