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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.
What is HA Congruence Theorem?
HA Congruence Theorem says: If the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and an acute angle of another right triangle, then the two right triangles are congruent.
What are the four congruence theorems for a right triangle?
The four congruence theorem for right triangles are:- LL Congruence Theorem --> If the two legs of a right triangle is congruent to the corresponding two legs of another right triangle, then the triangles are congruent.- LA Congruence Theorem --> If a leg and an acute angle of a right triangles is congruent to the corresponding leg and acute angle of another right triangle, then the triangles are congruent.- HA Congruence Theorem --> If the hypotenuse and an acute angle of a right triangle is congruent to the corresponding hypotenuse and acute angle of another triangle, then the triangles are congruent.- HL Congruence Theorem --> If the hypotenuse and a leg of a right triangle is congruent to the corresponding hypotenuse and leg of another right triangle, then the triangles are congruent.
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.
What is the hypotenuse angle theorem?
The hypotenuse angle theorem, also known as the HA theorem, states that 'if the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and an acute angle of another right triangle, then the two triangles are congruent.'
Is the hypotenuse always opposite an acute angle?
The hypotenuse is NEVER opposite an acute angle. It's always the side of the right triangle that's opposite the right angle.
What are the 2 triangle congruence theorems?
The two triangle congruence theorems are the AAS(Angle-Angle-Side) and HL(Hypotenuse-Leg) congruence theorems. The AAS congruence theorem states that if two angles and a nonincluded side in one triangle are congruent to two angles and a nonincluded side in another triangle, the two triangles are congruent. In the HL congruence theorem, if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, the two triangles are congruent.
How do you find sides of right triangle given only the hypotenuse and all angles?
One is the hypotenuse times the sine of one acute angle, the other, the hypotenuse times the sine of the other acute angle (or the cosine of the first).
What is LA Congruence Theorem?
LA Congruence Theorem says: If one leg and an acute angle of one right triangle are congruent to one leg and an acute angle of another right triangle, then the two right triangles are congruent.
What does the hypotenuse-angle theorem say?
If the hypotenuse and an acute angle of a right triangle are congruent to the correspondingparts of another right triangle, then the triangles are congruent.
What is degree of hypotenuse?
A triangle with an hypotenuse has a right angle that measures 90 degrees and two other acute angles,
Which angle has hypotenuse?
For a right angle triangle its hypotenuse is opposite its angle of 90 degrees and its other two angles are acute and its 3 angles add up to 180 degrees.
Which postulate theorem verifies the congruence of two right triangles?
RHS congruency, or, right angle, hypotenuse and corresponding side.
