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...
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...
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...
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....
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...
EngageNY
End-of-Module Assessment Task - Geometry (module 2)
Increase the level of assessment rigor with the test of performance tasks. Topics include similar triangles, trigonometric ratios, Law of Sines, Law of Cosines, and trigonometric problem solving.
Illustrative Mathematics
Tangent to a Circle From a Point
Learners see application of construction techniques in a short but sophisticated problem. Combining the properties of inscribed triangles with tangent lines and radii makes a nice bridge between units, a way of using...
Inside Mathematics
Rhombuses
Just what does it take to show two rhombuses are similar? The assessment task asks pupils to develop an argument to show that given quadrilaterals are rhombuses. Class members also use their knowledge of similar triangles to show two...
EngageNY
There is Only One Line Passing Through a Given Point with a Given Slope
Prove that an equation in slope-intercept form names only one line. At the beginning, the teacher leads the class through a proof that there is only one line passing through a given point with a given slope using contradiction. The 19th...
EngageNY
End-of-Module Assessment Task: Grade 8 Mathematics (Module 7)
It's time to discover what your classes have learned! The final lesson in the 25-part module is an assessment that covers the Pythagorean Theorem. Application of the theorem includes distance between points, the volume of...
EngageNY
Law of Cosines
Build upon the Pythagorean Theorem with the Law of Cosines. The 10th part of a 16-part series introduces the Law of Cosines. Class members use the the geometric representation of the Pythagorean Theorem to develop a proof of the Law of...
Charleston School District
Review Unit 8: Geometry Applicaitons
Pupils complete a review worksheet that highlights the key problems from the first eight lessons in the series. Topics include the Pythagorean Theorem and its converse, as well as finding volume of three-dimensional figures.