Question Video: Using the Axes of Symmetry of a Shape to Solve a Problem | Nagwa Question Video: Using the Axes of Symmetry of a Shape to Solve a Problem | Nagwa

# Question Video: Using the Axes of Symmetry of a Shape to Solve a Problem Mathematics • First Year of Preparatory School

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Segment πΆπ· has mirror symmetry in line π΄πΉ. Given that πΈπ· = 5 and π΅πΆ = 5.1, calculate the perimeters of π΄πΆπΉπ· and β³π΅πΆπ·.

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### Video Transcript

Segment πΆπ· has mirror symmetry in the line π΄πΉ. Given that πΈπ· is equal to five and π΅πΆ is equal to 5.1, calculate the perimeters of π΄πΆπΉπ· and triangle π΅πΆπ·.

As the line π΄πΉ is a line of symmetry, we know that the lengths of several sides will be equal. The length π΄πΆ will be equal to the length π΄π·. Both of these have length 6.7. The lengths π΅πΆ and π΅π· are also equal in length. We are told that π΅πΆ is equal to 5.1. Therefore, π΅π· is also equal to 5.1. The lengths πΈπ· and πΈπΆ are also equal in length. πΈπ· is equal to five. Therefore, πΈπΆ is also equal to five. Finally, the lengths π·πΉ and πΆπΉ are also equal. Weβre told in the diagram that πΆπΉ is equal to 8.2. Therefore, π·πΉ is also equal to 8.2.

The first perimeter weβre asked to calculate is that of π΄πΆπΉπ·. This is the outside of the shape. We can calculate this by adding the four lengths π΄πΆ, πΆπΉ, πΉπ· and π·π΄. π΄πΆ and π΄π· or π·π΄ are both equal to 6.7. πΆπΉ and πΉπ· or π·πΉ are both equal to 8.2. We need to add 6.7, 8.2, 8.2, and 6.7. 6.7 plus 8.2 is equal to 14.9. This means that 8.2 plus 6.7 is also equal to 14.9. 14.9 plus 14.9 or two times 14.9 is equal to 29.8. The perimeter of π΄πΆπΉπ· is 29.8.

We also need to calculate the perimeter of the triangle π΅πΆπ·. This is equal to the three lengths π΅πΆ, πΆπ· and π·π΅. This can be split into four lengths that we know, π΅πΆ, πΆπΈ, πΈπ· and π·π΅. π΅πΆ and π΅π· are both equal to 5.1. πΆπΈ and πΈπ· are both equal to five. We need to add 5.1, five, five, and 5.1. 5.1 plus five is equal to 10.1. We get the same answer when we add them the other way round. 10.1 plus 10.1 is equal to 20.2. The perimeter of triangle π΅πΆπ· is 20.2. Therefore, our two correct answers are 29.8 and 20.2.

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