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You can use a variety of postulates or theorems, among others:
SSS (Side-Side-Side)
ASA (Angle-Side-Angle - any two corresponding sides* and a corresponding angle)
SAS (Side-Angle-Side - the angle MUST be between the two sides, except:)
RHS (Right angle-Hypotenuse-Side - this is only ASS which works)
* if two corresponding angles are the same, then the third corresponding angle must also be the same (as the angles of a triangle always sum to 180°), and that can be substituted for one angle of ASA to get AAS or SAA.
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JordanOne of the postulates used to prove two triangles are congruent is the Side-Angle-Side (SAS) Postulate, which states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. Another postulate is the Angle-Side-Angle (ASA) Postulate, which states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. The Hypotenuse-Leg (HL) Theorem is another method used to prove right triangles are congruent, stating 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.
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How does sas theorem answer?
The SAS theorem is used to prove that two triangles are congruent. If the triangles have a side-angle-side that are congruent (it must be in that order), then the two triangles can be proved congruent. Using this theorem can in the future help prove corresponding parts are congruent among other things.
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.
Is this statement true or falseTo prove triangles similar using the Side-Side-Side Similarity Theorem, you must first prove that corresponding angles are congruent?
false
How would you prove triangles are congruent?
You could prove two triangles are congruent by measuring each side of both triangles, and all three angles of each triangle. If the lengths of the sides are the same, and so are the angles, then the triangles are congruent... if not, then the triangles are not congruent. If the triangles have the exact same size and shape then they are congruent.
Can the Third angle theorem prove that the ASS triangle is congruent?
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.
