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Crank
4 years ago
15

Hi everyone how are you today I have some question about congruence and I don’t understand can you help me please.

Mathematics
1 answer:
Vsevolod [243]4 years ago
8 0
You can understand this by two ways

1) through congruency rules

It says that triangle ABE is congruent to DCE
So the corresponding angles are equal
Eg
Angle A to Angle D
Angle B to angle C
Angle E to angle E

So they’re asking the angles AEB and DEC (which are equal as per congruency)

Thus you can equate them
4y-15=69
y=21

2) through vertically opposite angles
Since the triangles’ angles are vertically opposite one another, they are equal.

Then you can equate them the same way

Hope this helped!!
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Answer:

See below.

Step-by-step explanation:

ABC is an isosceles triangle with BA = BC.

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That makes angles ABD and ADB congruent.

Since m<ABD = 72 deg, then m<ADB = 72 deg.

Angles ADB and CDB are a linear pair which makes them supplementary.

m<ADB + m<BDC = 180 deg

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In triangle ABD, the sum of the measures of the angles is 180 deg.

m<A + m<ADB + m<ABD = 180 deg

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m<CBD = 36 deg

In triangle CBD, angles C and CBD measure 36 deg making them congruent.

Opposite sides DB and DC are congruent making triangle BCD isosceles.

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