Two Right Triangles have equal acute angles, yet one triangle is larger than the other. Therefore, the triangles much be _________________.
I've looked everywhere in my books and on the internet and I cant find it.
Ohh.. i think i get it. it would be similar because they are exactly the same yet one is slightly larger.
yes
All triangles contain acute angles?????
To understand why two right triangles can have equal acute angles but differ in size, let's first clarify a few concepts related to triangles.
When we talk about the size of a triangle, we typically refer to its area or its side lengths. In this case, since the question mentions that one triangle is larger than the other, we are likely referring to the difference in area.
Now, as for the acute angles, it is important to note that the size or length of a triangle is not solely determined by its angles. The size of a triangle is dependent on the lengths of its sides, and angles alone cannot determine the lengths of the sides.
In the case of two right triangles with equal acute angles, we can have triangles with different side lengths and therefore different areas. Here's an example to illustrate this:
Consider two right triangles, Triangle A and Triangle B, both having a 45-degree acute angle.
Triangle A:
- Has legs of length 3 units and 3 units.
- The area of Triangle A is (1/2) * base * height = (1/2) * 3 * 3 = 4.5 square units.
Triangle B:
- Has legs of length 6 units and 6 units.
- The area of Triangle B is (1/2) * base * height = (1/2) * 6 * 6 = 18 square units.
As you can see, both triangles have equal acute angles, but the lengths of their sides differ. Consequently, their areas also differ, with Triangle B having a larger area than Triangle A.
In conclusion, two right triangles can have equal acute angles but differ in size, specifically in terms of their areas or side lengths.
What is the difference between similar and congruent triangles?
They are similar.
because ALL triangles have and will always have 180 degrees.
BOTH of the right triangles have an 90 degrees angle, which leaves 90 degrees left in both triangles
than they have an another angle which is less than 90 (x degree) just by knowing this, you can say they are similar by Angle- Angle Similarity (AA~) or to get an AAA~ you find the 3rd angle which is, 90-x.
so in all the 3 angles of BOTH triangles are
90 degrees , x degrees, (90-x) degrees