EngageNY
Construct and Apply a Sequence of Rigid Motions
Breaking the rules is one thing, proving it is another! Learners expand on their previous understanding of congruence and apply a mathematical definition to transformations. They perform and identify a sequence of transformations and use...
EngageNY
The Definition of Sine, Cosine, and Tangent
Introduce your classes to a new world of mathematics. Pupils learn to call trigonometric ratios by their given names: sine, cosine, and tangent. They find ratios and use known ratios to discover missing sides of similar...
EngageNY
Special Lines in Triangles (part 2)
Medians, midsegments, altitudes, oh my! Pupils study the properties of the median of a triangle, initially examining a proof utilizing midsegments to determine the length ratio of a median. They then use the information to find missing...
EngageNY
Congruence Criteria for Triangles—SAS
Looking for a different approach to triangle congruence criteria? Employ transformations to determine congruent triangles. Learners list the transformations required to map one triangle to the next. They learn to identify congruence...
EngageNY
Unknown Angle Proofs—Proofs of Known Facts
Lead the class in a Greek history lesson plan with a geometric twist. Pupils relate a short video about geometric properties to modern-day methods of solving for unknown angles. They discuss parallel line theorems and...
EngageNY
Reflections
Facilitate creativity in your math class as individuals learn the definition of a geometric reflection and correctly construct a model, as well as its reflected image. They use a perpendicular bisector and circles to elaborate on...
EngageNY
Rotations
Searching for a detailed lesson to assist in describing rotations while keeping the class attentive? Individuals manipulate rotations in this application-based lesson depending on each parameter. They construct models depending on the...
EngageNY
Unknown Angle Proofs—Proofs with Constructions
Provide your emerging mathematicians with the tools to learn as they incorporate auxiliary lines to solve unknown angle proofs in this continuing segment. They decipher information from a diagram to uncover the missing pieces and...
EngageNY
The Angle-Angle (AA) Criterion for Two Triangles to Be Similar
What do you need to prove triangles are similar? Learners answer this question through a construction exploration. Once they establish the criteria, they use the congruence and proportionality properties of similar objects to find...
EngageNY
Using Trigonometry to Find Side Lengths of an Acute Triangle
Not all triangles are right! Pupils learn to tackle non-right triangles using the Law of Sines and Law of Cosines. After using the two laws, they then apply them to word problems.
EngageNY
Secant Lines; Secant Lines That Meet Inside a Circle
Young mathematicians identify different cases of intersecting secant lines. They then investigate the case where secant lines meet inside a circle.
EngageNY
Triangle Congruency Proofs (part 1)
Can they put it all together? Ninth graders apply what they know about proofs and triangle congruence to complete these proofs. These proofs go beyond the basic triangle congruence proofs and use various properties, theorems, and...
EngageNY
Arc Length and Areas of Sectors
How do you find arc lengths and areas of sectors of circles? Young mathematicians investigate the relationship between the radius, central angle, and length of intercepted arc. They then learn how to determine the area of sectors of...
EngageNY
The Side-Angle-Side (SAS) and Side-Side-Side (SSS) Criteria for Two Triangles to Be Similar
Playing with mathematics can invoke curiosity and excitement. As pupils construct triangles with given criteria, they determine the necessary requirements to support similarity. After determining the criteria, they practice...
EngageNY
Similarity
Learn similarity through a transformations lens! Individuals examine the effects of transformations and analyze the properties of similarity, and conclude that any image that can be created through transformations is similar. The...
EngageNY
Prove the Pythagorean Theorem Using Similarity
Amaze your classes with the ability to find side lengths of triangles immediately — they'll all want to know your trick! Learners use the Pythagorean Theorem and special right triangle relationships to find missing side lengths.
EngageNY
Properties of Area
What properties does area possess? Solidify the area properties that pupils learned in previous years. Groups investigate the five properties using four problems, which then provide the basis for a class discussion.
EngageNY
Unknown Angle Problems with Inscribed Angles in Circles
We know theorems about circles—now what? Class members prove a theorem, with half the class taking the case where a point is inside the circle and half the class taking the case where a point is outside the circle. The lesson plan then...
EngageNY
Arcs and Chords
You've investigated relationships between chords, radii, and diameters—now it's time for arcs. Learners investigate relationships between arcs and chords. Learners then prove that congruent chords have congruent arcs, congruent arcs have...
EngageNY
Congruence Criteria for Triangles—AAS and HL
How can you prove it? Guide classes through an exploration of two possible triangle congruence criteria: AAS and HL. Learners connect this criteria to those previous learned and also explore criteria that does not work. The activity...
EngageNY
Congruence Criteria for Triangles—ASA and SSS
How do you know if a pair of triangles are congruent? Use the lesson to help class members become comfortable identifying the congruence criteria. They begin with an exploration of ASA and SSS criteria through transformations and...
Houghton Mifflin Harcourt
Developing Formulas for Circles and Regular Polygons
Formulas and procedures for finding the area and circumference are not provided on this handout, so it will be best used as a practice of already-acquired skills. It is a well-rounded assignment, however, as it includes diagrams,...
West Contra Costa Unified School District
Pythagorean Theorem and Its Converse
Challenge scholars to prove the Pythagorean Theorem geometrically by using a cut-and-paste activity. They then must solve for the missing sides of right triangles.
Curated OER
Transformations and Matrices
There are four activities in this extensive lesson plan covering the identity matrix and scaling, the linear representation of translations, the linear representation of rotations, and reflections. In small groups, they use the Cabri II...
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