Illustrative Mathematics
Lines of Symmetry for Triangles
What can symmetry tell us about triangles? After looking at four examples, learners will come to realize that lines of symmetry are different for equilateral, isosceles, and scalene triangles. Use this guided practice activity as an...
Illustrative Mathematics
Right Triangles Inscribed in Circles II
So many times the characteristics of triangles are presented as a vocabulary-type of lesson, but in this activity they are key to unraveling a proof. A unique attack on proving that an inscribed angle that subtends a diameter must be a...
Curated OER
The Distance and Midpoint Formula
In this college level mathematics worksheet, students solve use the Pythagorean Theorem to find the missing side of a right triangle and explore the connection between the Pythagorean Theorem and the distance formula. Students also...
Curated OER
Points, Regions, Distance and Midpoints
In this college level coordinate geometry worksheet, students identify and graph points on a coordinate plane, find the missing side of a right triangle, determine the distance between two points, and find the midpoint of a line...
Curated OER
Finding the Area of an Equilateral Triangle
The problem seems simple: find the area of the equilateral triangle whose sides are each length 1. In fact, this same problem is solved in 8th grade, addressing a different Common Core standard, using the formula for area of a triangle...
Illustrative Mathematics
Joining Two Midpoints of Sides of a Triangle
Without ever using the actual term, this exercise has the learner develop the key properties of the midsegment of a triangle. This task leads the class to discover a proof of similar triangles using the properties of parallel lines cut...
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...
Willow Tree
Midpoint and Distance Formulas
The shortest distance between two points is a straight line. Learners use the Pythagorean Theorem to develop a formula to find that distance. They then find the midpoint using an average formula.
Virginia Department of Education
Similar Triangles
Pupils work in pairs to investigate what it takes to prove that two triangles are similar. They work through various shortcuts to find which are enough to show a similarity relationship between the triangles. Small groups work with the...
EngageNY
Special Lines in Triangles (part 1)
Allow your pupils to become the mathematicians! Individuals explore the properties of a midsegment of a triangle through construction and measurement. Once they figure out the properties, learners use them to draw conclusions.
Radford University
Distance and Midpoint Formulas in a Mall
Go for a walk in the mall. Pupils find distances between stores on a diagram of a mall on Quadrant I. The scholars also determine the midpoint between a store and an entrance to the mall to then create their own paths and determine their...
Virginia Department of Education
Distance and Midpoint Formulas
Small groups work through two guided activities to derive the distance and midpoint formulas for the coordinate plane. The activities begin with concrete examples and move to abstract.
Mt. San Antonio Collage
Isosceles Triangles and Special Line Segments
Under which conditions can a triangle be classified as isosceles? High schoolers practice identifying isosceles triangles and special line segments, including angle bisectors, medians of triangles, and perpendicular bisectors of sides of...
Mt. San Antonio Collage
Congruent Triangles Applications
Triangles are all about threes, and practicing proving postulates is a great way to get started. The first page of the worksheet provides a brief introduction of the different properties and postulates. The remaining pages contain...
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
Triangles
In this triangles worksheet, 10th graders solve 3 extensive informal geometry problems that involve triangles. First, they sketch a triangle, selecting 3 of the sides and constructing 3 midpoints. Students then draw each of 3 medians by...
Curated OER
Triangle Series
Your algebra learners emphasize the"geometric" in geometric series as they use a common ratio between algebraic terms and find that it corresponds to a repeated similarity transformation.
Radford University
Triangles in Parallelograms
What's the point of looking at triangles when trying to draw parallelograms? Given three non-collinear points, pupils determine and justify all possible points that would create a parallelogram. They then analyze the four triangles that...
Curated OER
Investigating Segments in a Right Triangle
High schoolers explore the concept of right triangles as they construct a right triangle using Cabri Jr. Learners find the midpoint of the hypotenuse and construct a line from the midpoint to the vertex of the right angle. They then...
Curated OER
Investigating Segments in a Triangle
Pupils investigate segments in a triangle by constructing a triangle using Cabri Jr. They construct segments within the triangle that lie on the midpoints of the triangle's sides. Learners then compare the slope of base of the triangle...
Curated OER
Exploring Centers of a Triangle: Part 2
Students model and solve a real-world problem by constructing the centroid of a triangle. They explore relationships of the medians of a triangle and investigate how the centroid partitions each of the medians. Students investigate...
Curated OER
Chapter 5 Final Review Extra Problems. Triangles
In this triangles worksheet, students identify the median, altitude, segment, angle bisector, perpendicular bisector and triangle midsegment of triangles. They find the perimeter of triangles. This three-page worksheet contains 8...
Curated OER
Informal Geometry
Middle and high schoolers solve and complete 29 various types of problems. First, they match each name with its correct formula. Then, students find the length of the missing side and the distance between the two points given. In...
Curated OER
Angles Activities
A series of geometry worksheets have mathematicians constructing, dissecting, overlapping, and measuring as they analyze angles in various contexts. Learners use symmetry and reflections in a compass rose to write instructions on...