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Ronch [10]
3 years ago
12

Prove that angle W is congruent to angle Y with a two column proof.

Mathematics
1 answer:
iren2701 [21]3 years ago
4 0

Statement 1: WXYZ is a kite

Reason 1: Given

Statement 2: WX = XY and WZ = YZ

Reason 2: Definition of a kite

Statement 3: XZ = XZ

Reason 3: Reflexive property

Statement 4: Triangle WXZ = Triangle YXZ

Reason 4: SSS Congruence

Statement 5: Angle W = Angle Y

Reason 5: CPCTC

-------------------------------------------------------------------------

Extra notes:

* A kite is a quadrilateral that has two pairs of adjacent congruent sides. In this case, WX and XY is one pair of congruent sides that are adjacent (ie next to each other). So that's why WX = XY. Similarly, WZ = YZ is the second pair of adjacent congruent sides.

* Draw in a segment from point X to point Z to help form two triangles. The two triangles are congruent as proven in statement 4. One triangle is a reflection over the line XZ to get the other triangle.

* Due to this reflection, angle W reflects over line XZ to get angle Y. Proving that angle W = angle Y

* SSS means "side side side", basically saying "you use three pairs of congruent sides to prove two triangles congruent".

* The acronym CPCTC stands for "corresponding parts of congruent triangles are congruent"

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On the second tringle there is x+20

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This means the second triangle is 5+20=25

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Hope this helps!

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We assume this is intended to mean ...

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If the intent is (x+10°) = 80°, then x=70°.

_____

<em>Comment on the numbers here</em>

Units need to be properly specified in problems of this nature. <em>As written</em>, we probably should assume that 10 is <em>radians</em>, and x is a large negative number, about -8.60374 (radians), or -492.958°.

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