0
Yes. Draw a triangle, then draw line through the top vertex that's parallel to the base. Now draw another point anywhere on that line, and draw sides that meet the edges of the base and the new point you've drawn. No matter where that point is on your line, you haven't changed the height, and you haven't changed the base, but the angles of the triangle have changed. Therefore, the two aren't congruent.
Add your answer:
Earn +20 pts
Is it true or false that two triangles that have the same base have the same area?
False. The equation for area of a triangle is 1/2 base x height. The height and the base would have to be the same for two triangles to have the same area.
What is altitude when speaking about triangles?
The altitude is the same as the height (h), which is parallel to the base (b).
Are two triangles congruent if they have same area?
Not necessarily. You find the area of a triangle with the formula 1/2*base*height=Area. Imagine two triangles, one with 3 inches for both the base and height, and one with 4.5 inches for the height and 2 inches for the base. Both of these triangles will have 9 sq. in. for their areas, but they are not congruent.
What does conguent mean?
The same
Do all triangles have the same formula of base multiplied by height divided by 2?
Yes - for calculating the area of any triangle - you either halve the base and multiply by the height - or - as you said half the height times the base. either way will work.
Why is that if 2 triangles have the same base they have the same area?
Only if the two triangles have the same base and height then they have the same area, because an area of a triangle OS the base times the height divided by two.
Is it true or false that two triangles that have the same base have the same area?
False. The equation for area of a triangle is 1/2 base x height. The height and the base would have to be the same for two triangles to have the same area.
What is altitude when speaking about triangles?
The altitude is the same as the height (h), which is parallel to the base (b).
Are two triangles congruent if they have same area?
Not necessarily. You find the area of a triangle with the formula 1/2*base*height=Area. Imagine two triangles, one with 3 inches for both the base and height, and one with 4.5 inches for the height and 2 inches for the base. Both of these triangles will have 9 sq. in. for their areas, but they are not congruent.
What does conguent mean?
The same
Do all triangles have the same formula of base multiplied by height divided by 2?
Yes - for calculating the area of any triangle - you either halve the base and multiply by the height - or - as you said half the height times the base. either way will work.
How is the area triangle related to the area of a rectangle?
two right triangles = full rectangle That is - if you multiply height times base of a triangle, the area will be 1/2 of a rectangle having the same height, and a width the same as the triangle base.
Do congruent triangles always have the same shape?
Yes, that's part of what the word congruent means. Not only do congruent triangles have the same shape they are of the same size, and you can move one of them over the other one so that it covers it exactly.Note that you cannot flip a triangle over and consider it conguent to another triangle.
What is the area formula for a parallelogram?
Area = Length x width It's the same as the area for a rectangle - base times height. If you think about it, a parallelogram is a rectangle with two triangles on either side - one with its base on top, one with its base on bottom. Through various identities, we know that these two triangles are congruent. So the area is the sum of the small rectangle plus the two triangles, which ends up being base times height.
How many different types of quadrilaterals can two congruent isosceles right triangles form if they share a side?
# The triangles are congruent, therefore triangle 1 has the same angles and lengths as triangle 2 # The triangles are isosceles, therefore two of the sides are the same length, and two of the angles are the same # The triangles are right, therefore the angle between base and height is 90 degrees Applying 2, and 3: A triangle that is both isosceles and right has the angles 45, 90, 45 degrees and the lengths base = height = hypotenuse / sqrt(2) Applying 1: Therefore, the triangles can share their base and heights with each other freely, but their hypotenuse can only be shared with each others hypotenuse. * If Triangle-1 shared it's hypotenuse with triangle-2's base, or height which are not the same size, the resulting shape would have five sides which is not a quadrilateral. So... # If triangle-1 shares its base with triangle-2's base, or if triangle 1 shares its height with triangle's 2 height, you are left with an equilateral triangle # If triangle-1 share its base with triangle-2's height, or if triangle 1 share its height with triangle's 2 base you are left with a trapezoid # If the triangles share a hypotenuse, you are left with a rectangle in which base = height. Otherwise known as a square There are three different types of quadrilaterals that can be made.
If you know the sum of the base and height of a triangle what is the area?
You can't tell from the information you have. There are an infinite number of triangles, with different areas, that all have the same sum of (base + height). The area of the triangle is (1/2) times (base) times (height). You need the product of (base) times (height). If you only know their sum, you have no way to find their product.
Can two triangles that have the same base always have the same area?
no
