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Each side of a square ABCD has length 1 unit. Points P and Q belongs to AB and DA respectively. The perimeter of triangle APQ is 2 units. Then angle PCQ is?
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Each side of a square ABCD has length 1 unit. Points P and Q belongs t...
Given:
- Each side of square ABCD has a length of 1 unit.
- Points P and Q belong to sides AB and DA, respectively.
- The perimeter of triangle APQ is 2 units.
To Find:
- The measure of angle PCQ.
Solution:
To solve this problem, we can use the properties of squares and triangles. Let's break it down step by step:
1. Draw the square ABCD:
Draw a square ABCD with sides of length 1 unit. Label the points as shown below:
A----P----B
| |
| |
D----Q----C
2. Calculate the length of sides AP and AQ:
Since each side of the square has a length of 1 unit, AP and AQ are also 1 unit each.
3. Calculate the length of side PQ:
The perimeter of triangle APQ is given as 2 units. Since AP and AQ are both 1 unit, the remaining side PQ must be 2 - 1 - 1 = 0 units. This means that points P and Q coincide, and triangle APQ degenerates to a line segment.
4. Identify the angle PCQ:
Since points P and Q coincide, angle PCQ is formed by the intersection of sides PC and CQ. Since these sides are part of the square, they are perpendicular to each other. Therefore, angle PCQ is a right angle, measuring 90 degrees.
Answer:
The angle PCQ measures 90 degrees.
- Each side of square ABCD has a length of 1 unit.
- Points P and Q belong to sides AB and DA, respectively.
- The perimeter of triangle APQ is 2 units.
To Find:
- The measure of angle PCQ.
Solution:
To solve this problem, we can use the properties of squares and triangles. Let's break it down step by step:
1. Draw the square ABCD:
Draw a square ABCD with sides of length 1 unit. Label the points as shown below:
A----P----B
| |
| |
D----Q----C
2. Calculate the length of sides AP and AQ:
Since each side of the square has a length of 1 unit, AP and AQ are also 1 unit each.
3. Calculate the length of side PQ:
The perimeter of triangle APQ is given as 2 units. Since AP and AQ are both 1 unit, the remaining side PQ must be 2 - 1 - 1 = 0 units. This means that points P and Q coincide, and triangle APQ degenerates to a line segment.
4. Identify the angle PCQ:
Since points P and Q coincide, angle PCQ is formed by the intersection of sides PC and CQ. Since these sides are part of the square, they are perpendicular to each other. Therefore, angle PCQ is a right angle, measuring 90 degrees.
Answer:
The angle PCQ measures 90 degrees.
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Each side of a square ABCD has length 1 unit. Points P and Q belongs t...
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Each side of a square ABCD has length 1 unit. Points P and Q belongs to AB and DA respectively. The perimeter of triangle APQ is 2 units. Then angle PCQ is?
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Each side of a square ABCD has length 1 unit. Points P and Q belongs to AB and DA respectively. The perimeter of triangle APQ is 2 units. Then angle PCQ is? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Each side of a square ABCD has length 1 unit. Points P and Q belongs to AB and DA respectively. The perimeter of triangle APQ is 2 units. Then angle PCQ is? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Each side of a square ABCD has length 1 unit. Points P and Q belongs to AB and DA respectively. The perimeter of triangle APQ is 2 units. Then angle PCQ is?.
Each side of a square ABCD has length 1 unit. Points P and Q belongs to AB and DA respectively. The perimeter of triangle APQ is 2 units. Then angle PCQ is? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Each side of a square ABCD has length 1 unit. Points P and Q belongs to AB and DA respectively. The perimeter of triangle APQ is 2 units. Then angle PCQ is? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Each side of a square ABCD has length 1 unit. Points P and Q belongs to AB and DA respectively. The perimeter of triangle APQ is 2 units. Then angle PCQ is?.
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