How can this be true triangles

Hanley Rd, Suite St. Louis, MO Subject optional. Email address: Your name:. Example Question 1 : Triangle Proofs. Possible Answers: No, they are not congruent. There is not enough information to answer this question.

Explanation : From the figure, we see that there are two congruent pairs of corresponding sides, , and one congruent pair of corresponding angles,. Report an Error. Example Question 2 : Triangle Proofs. Which of the following theorems prove that the following two triangles are congruent? Correct answer: Side-Side-Side Theorem.

Explanation : These two triangles share three corresponding congruent sides. Example Question 3 : Triangle Proofs. Which of the following pairs of triangles are congruent by the ASA Theorem? Possible Answers:. Correct answer:. Explanation : The Angle-Side-Angle Theorem ASA states that if two angles and their included side are congruent to two angles and their included side to another triangle, then these two triangles are congruent.

Example Question 4 : Triangle Proofs. Which of the following theorems would prove that the following two triangles are similar?

There is not enough information to determine these triangles are similar. Correct answer: AA Theorem. Explanation : When we look at this figure we see that we have two pairs of congruent corresponding angles,. Example Question 5 : Triangle Proofs. Are the following two triangles similar? If so, which theorem proves this to be true? Yes, these triangles are similar by the AA Similarity Theorem.

There is not enough information to determine if these triangles are similar or not. Explanation : The Side-Side-Side Similarity Theorem states that if all three sides of one triangle are proportional to another, then these triangles are similar.

Example Question 6 : Triangle Proofs. True or False: Side-Side-Angle is a proven theorem to prove triangle congruence. Possible Answers: True. Correct answer: False. Example Question 7 : Triangle Proofs. Explanation :.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion. In other words, similar triangles are the same shape, but not necessarily the same size.

The triangles are congruent if, in addition to this, their corresponding sides are of equal length. The side lengths of two similar triangles are proportional.

The "swinging" nature of , creating possibly two different triangles, is the problem with this method. Since this situation is open to two interpretations, it is referred to as the Ambiguous Case. This is a reference we will be examining further in trigonometry. If the side which lies on one ray of the angle is longer than the other side, and the other side is less than the minimum distance needed to create a triangle, no triangle can be drawn.

Since no triangles are possible, no congruent triangles are possible. Since the SSA or ASS method allows for the possibility of creating triangles of various shapes or even no triangles at all , this method is not an universal method for proving triangles congruent. When triangles are congruent, one triangle can be moved through one, or more, rigid motions to coincide with the other triangle. All corresponding sides and angles will be congruent.

When triangles are congruent, six facts are always true. HL Hypotenuse-Leg. The "included angle" in SAS is the angle formed by the two sides of the triangle being used. The "included side" in ASA is the side between the angles being used. It is the side where the rays of the angles overlap.