PQR is an isosceles triangle in which PQ = PR
1 answer:
Answer and Step-by-step explanation: Congruent triangles are triangles with the same three sides and same three angles.
There many ways to determine if 2 triangles are congruent.
One of them is <u>ASA</u> or <u>Angle, Side, Angle</u> and it means that if two angles and the included side of one triangle are equal to the corresponding angles and side on the other triangle, they are congruent.
In this case, angle MRQ and angle NQR are equal. The included side of both triangles are the same QR, so it can be concluded that <em><u>triangle QNR is congruent to triangle RMQ.</u></em>
The image in the attachment shows the angles and their included side, which are colored.
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Here is the answer , and the explanation is written with it .
Answer:
EG is 19 units
Step-by-step explanation:
Let us solve the question
∵ Lines CD and EF intersected at point G
∴ CD = CG + GD
∴ EF = EG + GF
∵ Line EF bisects line CD
→ That means G is the midpoint of CD
∴ CG = GD
∵ CG = 5x -1
∵ GD = 7x - 13
→ Equate them to find x
∴ 7x - 13 = 5x -1
→ Add 13 to both sides
∴ 7x -13 + 13 = 5x - 1 + 13
∴ 7x = 5x + 12
→ Subtract 5x from both sides
∴ 7x - 5x = 5x - 5x + 12
∴ 2x = 12
→ Divide both sides by 2
∴
∴ x = 6
∵ EF = 6x - 4
→ Substitute x by 6 to find its length
∴ EF = 6(6) - 4 = 36 - 4
∴ EF = 32
∵ EF = EG + GF
∵ GF = 13
∴ 32 = EG + 13
→ Subtract 13 from both sides
∵ 32 - 13 = EG + 13 - 13
∴ 19 = EG
∴ EG = 19 units