It is possible to prove the a square is a rectangle. Prior to we get started with the proofs, let"s review what is special about rectangles. First, we recognize that rectangles are parallelograms, so...
You are watching: Prove that a rectangle has congruent diagonals
Let"s view why we can insurance claim that the diagonals are congruent. Right here is a sample proof:
Given: square ABCD is a rectangle.Prove: AC ≅ BD
|AD ≅ BC||an interpretation of Rectangle|
|DC ≅ DC||Reflexive property|
|congruent and right angles||meaning of Rectangle|
|ΔBCD ≅ ΔADC||Side, Angle, side|
|AC ≅ BD||CPCTC|
Showing the the diagonals space congruent is a an excellent way to present that a number is a rectangle as soon as you currently know the the figure is a parallelogram. Other methods would encompass showing that the shape has actually 4 best angles. If you already know that the form is a parallelogram, you will certainly only have to display that one of the angle is a right angle and then it would follow that every one of the angles are best angles.Example:Prove that the following four clues will type a rectangle when linked in order.
Step 1: Plot the clues to obtain a intuitive idea of what you are working with.
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Step 2:Prove the the number is a parallelogram.There are 5 different ways come prove that this shape is a parallelogram. Select one the the methods.
In this example, us will show that both pairs of the contrary sides are parallel. To perform this we have to calculate the steep of each side. If us can present that the slopes of opposing sides space the same, then the the contrary sides room parallel.Recall that the slope can be determined using m =
Slope of abdominal =
Slope of CD =
Slope the BC =
Slope of ad =
The slopes that the opposites to be the same, for this reason ABCD is a parallelogram.Step 3: Next, prove that the parallel is a rectangle. We have the right to do this by reflecting that the the diagonals room congruent or by showing that among the angles is a right angle.It may be less complicated to present that among the angle is a right angle due to the fact that we have already computed every one of the slopes. We can show that abdominal muscle is perpendicular to BC due to the fact that the slopes are an adverse reciprocals of every other.
and because these two segments are perpendicular,
|Related Links:Math GeometryTrianglesCongruent Triangles|