Geometry with isosceles triangles

In summary, we are looking to prove that CD is perpendicular to AB, which means that CD forms right angles with AB. To do this, we can construct a plane that is perpendicular to AB and contains the midpoint O of AB. This plane will have the special property of intersecting AB at a right angle, thus proving that CD is perpendicular to AB.
  • #1
Britney2
3
0
2 isosceles triangles ABC and ABD have the same base AB but are in different planes.
Prove that CD is perpendicular to AB.

(It must be proved that CD is perpendicular to one of the planes and then it is perpendicular with every segment of this plane.)
Thanks in advance!
 
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  • #2


Consider point O, the midpoint of AB. Construct a plane that is perpendicular to AB and contains point O. What special property does this plane have?
 
  • #3


Frankly, that seems to me to use a non-standard definition of "perpendicular".

To me the standard definition of perpendicular is "lines p and q are perpendicular if and only if they meet forming right angles." For this two be true we must also allow two skew lines to be perpendicular as long as the projection of one onto a plane containing the other intersects it forming right angles.
 

FAQ: Geometry with isosceles triangles

What is an isosceles triangle?

An isosceles triangle is a type of triangle that has two sides that are equal in length. This means that the two angles opposite the equal sides are also equal in measure.

What are the properties of an isosceles triangle?

The properties of an isosceles triangle include having two equal sides and two equal angles. The base angles, which are the angles opposite the equal sides, are also congruent. Additionally, the altitude (height) of an isosceles triangle bisects the base and the two congruent sides are also congruent.

How do you determine the perimeter of an isosceles triangle?

To find the perimeter of an isosceles triangle, you can simply add the lengths of all three sides together. However, since two sides are equal in length, you can also use the formula P = 2s + b, where P is the perimeter, s is the length of one of the equal sides, and b is the length of the base.

What is the area formula for an isosceles triangle?

The area of an isosceles triangle can be found using the formula A = (1/2)bh, where A is the area, b is the length of the base, and h is the height or altitude of the triangle. The height can be found by drawing a perpendicular line from the vertex opposite the base to the base itself.

Can an isosceles triangle also be a right triangle?

Yes, an isosceles triangle can also be a right triangle. In this case, one of the base angles will be a right angle (90 degrees) and the other two angles will be acute angles. The Pythagorean Theorem can be used to find the length of the third side (the non-equal side) in a right isosceles triangle.

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