0
If the hypotenuses of two right triangles are equal then are the other two sides of the respective triangles also equal?
K10krist
The other two sides may be equal, but they do not have to be equal. For example: 3, 4, 5 and sqrt(25/2), sqrt(25/2), 5. Here sqrt is short for square root. Also 15, 20, 25 and 7, 24, 25.
Wiki User
∙ 15y ago
Add your answer:
Earn +20 pts
How can you say that if areas of two triangles are equal then they are congruent?
In order for a triangle to be congruent the two triangles have to be the same shape and size, thus they are congruent if they can be moved into an isometry or any other combination. But you're asking how a question which has two possibilities. Assuming that you have two triangles whose sides are equivalent which makes the areas equal to each other then you can state the side-side-side rule which is if the three sides of one triangle is equivalent to the other three sides of the other triangle then they are congruent. But if you have an angle present in the triangles you could argue the angle angle side rule, but if the angles are joint you would argue the angle side angle. But if one triangle has one degree and the other one has a different degree then they will not be congruent.
Do a parallelograms diagonals bisect each other?
I can't offer a full proof, but I can suggest some possibilities that will lead you to your proof. In a parallelogram, you can easily demonstrate that the angles formed by a cord extending between parallel lines and the parallel lines themselves, and that are formed on opposite sides of the cord, are equal. This will work for both pairs of triangles in the parallelogram, and can be applied to all of the angles at the corners of the parallelogram. This will lead you to demonstrating that the pairs of triangles "pointing" to each other (not adjacent pairs) are similar, and in fact congruent. From there it is not difficult to establish that the connected sections of the two interior cords are equal.
What are the theorems and postulates you can use to prove triangles are congruent?
Pythagorean's Theorem is one of the most famous ones. It says that the two squared sides of a right triangle equal the squared side of the hypotenuse. In other words, a2 + b2 = c2
Is a quadrilateral a parallelogram if both pairs of opposite sides are equal?
Yes.Although the definition of a parallelogram is "a quadrilateral with both pairs of opposite sides parallel", the only way for a quadrilateral to include opposite sides of equal length is if the included angles are the same, and hence the sides are parallel.(Hint : draw a diagonal to a parallelogram. You can show that one of the two triangles formed is the mirror image of the other, which immmediately proves that each pair of opposite sides is equal.)
How do you prove that the diagonals and either base of an isosceles trapezoid form an isosceles triangle?
Consider the isosceles trapezium ABCD (going clockwise from top left) with AB parallel to CD. And let the diagonals intersect at O Since it is isosceles, AD = BC and <ADC = <BCD (the angles at the base BC). Now consider triangles ADC and BCD. AD = BC The side BC is common and the included angles are equal. So the two triangles are congruent. and therefore <ACD = <BDC Then, in triangle ODC, <OCD (=<ACD = <BDC) = <ODC ie ODC is an isosceles triangle. The triangle formed at the other base can be proven similarly, or by the fact that, because AB CD and the diagonals act as transversals, you have equal alternate angles.
To use the HL theorem to prove two triangles are congruent the triangles must be right trianglesWhich other conditions must also be met?
1. There are two right triangles. 2. They have congruent hypotenuses. 3. They have one pair of congruent legs.
How do you make a triangle with 2 triangles and 1 rectangle?
If the 2 triangles are right triangles, which are congruent to slicing the rectangle on the diagonal, then arrange one on top of the rectangle, and the other to the side, so that the two hypotenuses are in line with each other. This will make a bigger right triangle, which is similar to the smaller right triangles - each side is double of the smaller triangles.
What is RHS postulate?
It is a postulate concerning congruent triangles. Two triangles are congruent if the are both right angled (R), their hypotenuses are the same length (H) and one of the sides of one triangle is congruent to a side of the other (S).
Can you make a rectangle out of two triangles and a square?
Sure, place a triangle's hypotenuse (longest side) on the other triangle's hypotenuse, that will give either a square or a rectangle. Then place the square on one end of the rectangle. For this to work though, the length of the square's side HAS to equal the length of the triangles hypotenuses, and likewise each triangle's hypotenuse much equal the length of a side of the square. Hope this is clear.
Why are angles equal when sides are equal?
This is only true of triangles. Rhombi and other "squashed" polygons with more than three sides show that it is not true otherwise. The two equal sides meet at an angle. It can be shown that the bisector of that angle divides the triangle into two triangles with one set of equal sides, one common side and these sides define angles of equal measure. So by SAS, the two triangle are congruent and so the angles in question are equal. Alternatively, you could prove (as easily) that the altitude from that angle divides the original triangle into two right angled triangles with a common side and equal hypotenuses. Again congruence resulting in the equality of the angles as required.
Can all isosceles triangles be equilateral triangles?
No, not all isoceles triangles can be equilateral triangles because an equilateral triangle has sides that are all equal to each other and an isoceles triangle has only two sides that are equal to each other.
What angles are equal in similar triangles?
If the triangles are similar, then each of the three angles in one of them is equal to the corresponding angle in the other one.
Some equilateral triangles are not isoscles?
They are both different types of triangles one has 3 equal sides and the other has 2 equal sides.
Are angles in an isoceles triangle equal?
Isosceles triangles have at least 2 equal angles. The 3rd angle can either be equal to the other two (it's then called an equilateral triangle), or it can be different from the two equal angles, in which case it's an isosceles triangle. All equilateral triangles are isosceles triangles, but not all isosceles triangles are equilateral triangles.
Do triangles have all equal sides?
only equilateral triangles the other three, scalene isosceles and right angled, do not
Do isosceles triangles have all equal sides?
Some people classify isosceles triangles as having at least two equal sides, while other say that they must have exactly two equal sides. So, depending on your definition, some isosceles triangles may have all equal sides, but equilateral triangles always have three equal sides.
Does Triangle has three equal sides?
Not all. Only equilateral triangles have. Equilateral triangles have equal sides and 60 degrees on each corner of the triangle. Other triangle need not have equal sides.
