Inside Mathematics
Circles in Triangles
Challenge the class with inscribed circles in triangles. The assessment task requests class members use their knowledge of circles and right triangles to prove two triangles are congruent. They go on to utilize their knowledge of...
Curated OER
Right Triangle congruence
Students will determine if two triangles are congruent and which property is used. In this lesson on right triangles, students will determine what additional information is need to make a pair of triangles congruent.
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Proof of the Pythagorean Theorem Using Transformations
Middle and high schoolers construct a triangle using Cabri Jr. They construct squares on each of the legs and hypotenuse of the triangle. Pupils show that the area of the squares on the leg equal the area of the square on the hypotenuse.
EngageNY
The Converse of the Pythagorean Theorem
Is it a right triangle or not? Introduce scholars to the converse of the Pythagorean Theorem with a lesson that also provides a proof by contradiction of the converse. Pupils use the converse to determine whether triangles with given...
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A Different Proof of the Law of Cosines
For this proofs worksheet, students construct 1 proof of the law of cosines. Students construct a right triangle within a circle to prove the law of cosines.
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Right Triangles
In this right triangles learning exercise, 10th graders solve 6 various problems and figures related to right triangles. First they identify and describe the 3 theorems and 1 postulate stated that prove 2 right triangles congruent if one...
Illustrative Mathematics
Applying the Pythagorean Theorem in a Mathematical Context
Participants who use this resource will apply the Pythagorean Theorem to show whether or not the shaded triangle inscribed in a rectangle is a right triangle. Once all of the sides on the shaded triangle are found, it is important that...
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Right Triangles
In this right triangles worksheet, 10th graders solve 5 problems that relate to different right triangles. First, they find the values of x and y so that each triangle is congruent to the other. Then, students write a two-column proof...
Charleston School District
Pythagorean Theorem and Converse
You've heard that it is true, but can you prove it? Scholars learn the Pythagorean Theorem through proof. After an overview of proofs of the theorem, learners apply it to prove triangles are right and to problem solve. This is the second...
Curated OER
Proofs
In this geometric proof instructional activity, students compose 20 triangle congruency proofs. Students will decide if there is enough information in problems 1-6 to prove if any triangles are congruent. In problems 17 to 20, students...
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Indirect Proof and Inequalities in one Triangle
In this geometry worksheet, 10th graders complete an indirect proof and order the sides or angles of a triangle. Also, students determine if a triangle can have sides with the given lengths. The two page worksheet contains twelve...
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Proofs Of The Pythagorean Theorem?
Even U.S. President James Garfield had his own proof of the Pythagorean Theorem! Pupils consider three different attempts at a geometric proof of the Pythagorean Theorem. They then select the best proof and write paragraphs detailing...
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Analyzing Congruence Proofs
Looking at numerous examples of triangles, each with different properties, geometers develop their understanding of congruency. They use the notation of a counter-example to disprove certain conjectures and prove geometric theorems and...
Math Worksheets Center
Congruent Triangle Proofs Quiz
A congruent triangles quiz challenges teenage mathematicians to complete a pair of geometric proofs. Each problem includes a picture of the triangles in question, a given set of information, and the five steps needed to finish the proof....
Curated OER
Triangles and Congruence
Can your class construct triangles and determine congruence? Find out with this well put together worksheet. THey construct triangles to given specifications and identify if they are congruent. There are 3 muti-step problems to solve.
Virginia Department of Education
Pythagorean Theorem
Investigate the meaning of the Pythagorean Theorem through modeling. After comparing the area of the square of each side, individuals cut triangles and squares to facilitate the comparison.
EngageNY
Law of Sines
Prove the Law of Sines two ways. The ninth segment in a series of 16 introduces the Law of Sines to help the class find lengths of sides in oblique triangles. Pupils develop a proof of the Law of Sines by drawing an altitude and a second...
Geometry Accelerated
Accelerated Geometry Review Sheet
Your geometry learners use their knowledge of various geometric concepts to write proofs. Starting with givens containing parallel line segments with transversals and triangles and quadrilaterals, and the mid-point and distance formulas;...
Curated OER
Special Segments in a Triangle
In this geometry worksheet, 10th graders review the vocabulary associated with the special segments of a triangle and the associated points of concurrency and solve problems in which they find the indicated missing angle or...
Curated OER
Indirect Proof and Inequalities in One Triangle
In this geometry worksheet, 10th graders order the sides and angles of a triangle and determine the range of the third side of a triangle given the lengths of two sides. The one page worksheet contains sixteen questions. ...
Curated OER
Coordinate Geometry Proofs
In this coordinate geometry worksheet, 10th graders solve and draw 10 different problems related to complete proofs in coordinate geometry. First, they prove that a figure with given points is another figure by using slopes. Then,...
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Proving Triangles Congruent
In this proving triangles congruent instructional activity, 10th graders solve 4 different proofs for congruent triangles. First, they mark all congruent parts on each figure, then complete the prove statement and identify the postulate...
Curated OER
Proving Triangles Congruent
In this proving triangles congruent activity, 10th graders solve 5 different problems that include proofs and proving congruence in triangles. First, they determine which postulate can be used to prove the triangles congruent and mark...
Curated OER
Proofs with Triangles
In this geometry worksheet, students prove triangle congruence by making statements with reasons and concluding with the AAS or HL theorem. There are 2 proofs.