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Can the Third angle theorem prove that the ASS triangle is congruent?
Wiki User
∙ 11y ago
No, because the third-angle theorem requires that you know two angles of each of the triangles. Assuming ASS, you only know one angle.
In fact, two triangles may have the same ASS and not be congruent. See if you can make two non-congruent triangles with Angle 60 deg, Side 10, and Side 9.
Wiki User
∙ 11y ago
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What is the Hinge Theorem is based on?
SAS Inequality Theorem the hinge theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle.
What are the four congruence theorem for right triangle?
four types aressssasrhsasa1.HyL Theorem (Hypotenuse-Leg) - if the hypotenuse and leg of one triangle is congruent to another triangle's hypotenuse and leg, then the triangles are congruent.2.HyA (Hypotenuse-Angle) - if the hypotenuse and angle of one triangle is congruent to another triangle's hypotenuse and angle, then the triangles are congruent.3.LL (Leg-Leg) if the 2 legs of one triangle is congruent to another triangle's 2 legs, then the triangles are congruent.4.LA (Leg-Angle) if the angle and leg of one triangle is congruent to another triangle's angle and leg, then the triangles are congruent.
The SAS Similarity Theorem states that if an angle of one triangle is congruent to an angle of another triangle, and if the lengths of the sides including these angles are proportional, then the trian?
congruent
What are four ways you can prove two right triangles are congruent?
1. The side angle side theorem, when used for right triangles is often called the leg leg theorem. it says if two legs of a right triangle are congruent to two legs of another right triangle, then the triangles are congruent. Now if you want to think of it as SAS, just remember both angles are right angles so you need only look at the legs.2. The next is the The Leg-Acute Angle Theorem which states if a leg and an acute angle of one right triangle are congruent to the corresponding parts of another right triangle, the two right triangles are congruent. This is the same as angle side angle for a general triangle. Just use the right angle as one of the angles, the leg and then the acute angle.3. The Hypotenuse-Acute Angle Theorem is the third way to prove 2 right triangles are congruent. This one is equivalent to AAS or angle angle side. This theorem says if the hypotenuse and an acute angle of a right triangle are congruent to the hypotenuse and an acute angle of another right triangle, the two triangles are congruent. This is the same as AAS again since you can use the right angle as the second angle in AAS.4. Last, but not least is Hypotenuse-Leg Postulate. Since it is NOT based on any other rules, this is a postulate and not a theorem. HL says if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.
What is side angle angle theorem?
Any two angles of a triangle determine the third angle. As a result, the side angle angle theorem is equivalent to the angle side angle theorem.
What is the Third angle theorem?
If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.
What is the Hinge Theorem is based on?
SAS Inequality Theorem the hinge theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle.
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.
What is the hinge theorem?
The hinge theorem in geometry states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle
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 are right triangle congruence theorem?
1.HyL Theorem (Hypotenuse-Leg) - if the hypotenuse and leg of one triangle is congruent to another triangle's hypotenuse and leg, then the triangles are congruent. 2.HyA (Hypotenuse-Angle) - if the hypotenuse and angle of one triangle is congruent to another triangle's hypotenuse and angle, then the triangles are congruent. 3.LL (Leg-Leg) if the 2 legs of one triangle is congruent to another triangle's 2 legs, then the triangles are congruent. 4.LA (Leg-Angle) if the angle and leg of one triangle is congruent to another triangle's angle and leg, then the triangles are congruent.
What are the four congruence theorem for right triangle?
four types aressssasrhsasa1.HyL Theorem (Hypotenuse-Leg) - if the hypotenuse and leg of one triangle is congruent to another triangle's hypotenuse and leg, then the triangles are congruent.2.HyA (Hypotenuse-Angle) - if the hypotenuse and angle of one triangle is congruent to another triangle's hypotenuse and angle, then the triangles are congruent.3.LL (Leg-Leg) if the 2 legs of one triangle is congruent to another triangle's 2 legs, then the triangles are congruent.4.LA (Leg-Angle) if the angle and leg of one triangle is congruent to another triangle's angle and leg, 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.'
The SAS Similarity Theorem states that if an angle of one triangle is congruent to an angle of another triangle, and if the lengths of the sides including these angles are proportional, then the trian?
congruent
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 four ways you can prove two right triangles are congruent?
1. The side angle side theorem, when used for right triangles is often called the leg leg theorem. it says if two legs of a right triangle are congruent to two legs of another right triangle, then the triangles are congruent. Now if you want to think of it as SAS, just remember both angles are right angles so you need only look at the legs.2. The next is the The Leg-Acute Angle Theorem which states if a leg and an acute angle of one right triangle are congruent to the corresponding parts of another right triangle, the two right triangles are congruent. This is the same as angle side angle for a general triangle. Just use the right angle as one of the angles, the leg and then the acute angle.3. The Hypotenuse-Acute Angle Theorem is the third way to prove 2 right triangles are congruent. This one is equivalent to AAS or angle angle side. This theorem says if the hypotenuse and an acute angle of a right triangle are congruent to the hypotenuse and an acute angle of another right triangle, the two triangles are congruent. This is the same as AAS again since you can use the right angle as the second angle in AAS.4. Last, but not least is Hypotenuse-Leg Postulate. Since it is NOT based on any other rules, this is a postulate and not a theorem. HL says if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.
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.
