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Yes. If you know two angles of a triangle, then you know all three. Why? Because they sum to 180 deg. So you have the hypotenuse and the angles at either end then you have ASA. AAS may not be sufficient for congruence but ASA IS.
Another way of looking at it: suppose the hypotenuse is h and the known acute angle is x. Then, the side adjacent to the angle is h*cos(x) while the side opposite is h*sin(x).
So the two hypotenuses are of length h, the two sides adjacent to the known acute angle are h*cos(x) each and the sides opposite are h*sin(x). And all three pairs of angles are equal. What else do you need to show congruence?
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Which are congruence theorems for right triangles?
The congruence theorems for right triangles are the Hypotenuse-Leg (HL) theorem and the Leg-Acute Angle (LA) theorem. The HL theorem states that if the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent. The LA theorem states that if one leg and one acute angle of one right triangle are congruent to one leg and one acute angle of another right triangle, then the triangles are congruent.
In a right triangle the ratio of the length of the side opposite an acute angle to the length of the hypotenuse?
sin θ : 1 = the length of opposite side to angle θ : the length of the hypotenuse
Angle-angle-angle guarantees congruence between two triangles?
No it doesn't. It guarantees similarity, but not congruence.
How do you determine which is the adjacent side of a right triangle?
There are three sides, hypotenuse, opposite and adjacent. But the adjacent and opposite are not fixed sides: it depends on which of the two acute angles you are examining.For either of the non-right angles, the adjacent side is the one which forms the angle, along with the hypotenuse. For the given angle θ, the length of the adjacent side compared to the hypotenuse (adjacent/hypotenuse) is the cosine (cos θ).
If angle 3 is actue what is the other angles?
The question appears to relate to the angles of a triangle. 1) If angle 3 is acute then the other two angles can also be acute. In the case of an equilateral triangle all three angles are equal and acute. 2) If angle 3 is acute and one other angle is obtuse then the remaining angle is acute. 3) If angle 3 is acute and one other angle is a right angle then the remaining angle is acute.
