WEBVTT
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Given that triangle π
ππ is congruent to triangle πππ, find the values of π₯ and π¦.
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When weβre given a congruency relationship between two triangles, we can use the order of the letters to help us identify congruent angles.
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If we take angle π
in triangle π
ππ, we could see that this is congruent to angle π in triangle πππ.
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Angle π in triangle π
ππ, or more specifically angle π
ππ, is congruent with angle π in triangle πππ.
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Our final third angle in each triangle, angle π in triangle π
ππ and angle π in triangle πππ, are also congruent.
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So to find the angle π₯, we know that this equates to angle π.
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This will be congruent to angle π
in triangle π
ππ.
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We donβt know the value of angle π
.
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But we can work it out using a key fact about the angles in a triangle.
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And that is that the angles in a triangle add up to 180 degrees.
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And therefore, to find angle π
in triangle π
ππ, we have 180 degrees subtract 29 degrees and subtract 90 degrees, which gives us 61 degrees.
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So now we know that angle π
is 61 degrees.
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And therefore, the congruent angle π must also be 61 degrees.
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So π₯ must be equal to 61.
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Notice that we donβt need to include the degree symbol since it was already given to us.
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We could also have solved for π₯ by recognising that angle π is also 29 degrees since itβs congruent to angle π in triangle π
ππ.
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And then calculate it using the angle sum in our triangle.
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To find the value of π¦, for the next part of the question, we need to look at the congruent sides in our triangles.
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We know that since the line ππ is in both triangles, then this is a congruent side in each triangle.
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The line π
π in triangle π
ππ is congruent to the line ππ in triangle πππ.
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We could also see this from the pattern in the letters in each triangle.
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And finally, we can say that line π
π in triangle π
ππ is congruent to line ππ in triangle πππ.
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Since weβre told that the line ππ is 42 and the line π
π is two π¦ minus four, then we can set these equal and solve for π¦.
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We have two π¦ minus four equals 42.
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So rearranging by adding four will give us two π¦ equals 42 plus four, which is 46.
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We then divide both sides of the equation by two, to give π¦ equals 23.
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Therefore, our final answer is π₯ equals 61, π¦ equals 23.