Use two 2-Column proofs to show that either diagonal of a rectangle will create two congruent triangles?

Mathematics

1 answer:

tangare [24]3 years ago

6 0

<span>Given: Rectangle ABCD
Prove: ∆ABD≅∆CBD
Solution:

<span> Statement Reason
</span>
ABCD is a parallelogram Rectangles are parallelograms since the definition of a parallelogram is a quadrilateral with two pairs of parallel sides.

Segment AD = Segment BC The opposite sides of a parallelogram are Segment AB = Segment CD congruent. This is a theorem about the parallelograms.

</span>∆ABD≅∆CBD SSS postulate: three sides of ΔABD is equal to the three sides of ∆CBD<span>

</span><span>Given: Rectangle ABCD
Prove: ∆ABC≅∆ADC
</span>Solution:

<span> Statement Reason
</span>
Angle A and Angle C Definition of a rectangle: A quadrilateral
are right angles with four right angles.

Angle A = Angle C Since both are right angles, they are congruent

Segment AB = Segment DC The opposite sides of a parallelogram are Segment AD = Segment BC congruent. This is a theorem about the parallelograms.

∆ABC≅∆ADC SAS postulate: two sides and included angle of ΔABC is congruent to the two sides and included angle of ∆CBD

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vekshin1

Answer:

Step-by-step explanation:

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vladimir2022 [97]

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<h2>Explanation:</h2><h2></h2>

Hello! remember you have to write complete questions in order to get good and exact answers. Here I'll explain this in a general way assuming the following table:

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As you can see, x increases in steps of 1 units. So let's check the difference in y:

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So we have a constant difference and we can conclude the table represents a line. Since the line passes through then y is directly proportional to x, so we can write:

$y=kx \\ \\ Where: \\ \\ k \ is \ constant \ of \ proportionality \ or \ the \ slope$