Learning Activity

Why is it Special? Verifying Relationships of Right Triangles

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

In this Desmos activity, students are guided through a series of questions to verify the relationships between the sides and angles of a 30°-60°-90° right triangle and a 45°-45°-90° triangle. This is intended to be a during activity for a lesson on discovering and applying relationships in similar right triangles. 

This activity results from the ALEX Resource Development Summit.

Mathematics (2019) Grade(s): 09-12 - Geometry with Data Analysis

MA19.GDA.35

Discover and apply relationships in similar right triangles.

Unpacked Content

UP:MA19.GDA.35

Vocabulary

  • Side ratios
  • Trigonometric ratios
  • Sine
  • Cosine
  • Tangent
  • Secant
  • Cosecant
  • Cotangent
  • Complementary anglesconverse

Knowledge

Students know:
  • Techniques to construct similar triangles.
  • Properties of similar triangles.
  • Methods for finding sine and cosine ratios in a right triangle (e.g., use of triangle properties: similarity. Pythagorean Theorem. isosceles and equilateral characteristics for 45-45-90 and 30-60-90 triangles and technology for others).
  • Methods of using the trigonometric ratios to solve for sides or angles in a right triangle.
  • The Pythagorean Theorem and its use in solving for unknown parts of a right triangle.

Skills

Students are able to:
  • Accurately find the side ratios of triangles.
  • Explain and justify relationships between the side ratios of a right triangle and the angles of a right triangle.

Understanding

Students understand that:
  • The ratios of the sides of right triangles are dependent on the size of the angles of the triangle.
  • The sine of an angle is equal to the cosine of the complement of the angle.
  • Switching between using a given angle or its complement and between sine or cosine ratios may be used when solving contextual problems.

Phase

During/Explore/Explain
Learning Objectives

Learning Objectives

Students will be able to use the Pythagorean Theorem to solve find the relationships between the sides and angles in a 30°-60°-90° right triangle and a 45°-45°-90° triangle.  

Activity Details

  1. Direct each student to the Desmos learning activity, What Makes It Special? Verifying Relationships.
  2. Instruct the students to follow and answer the prompts provided in the activity independently.  
  3. Remind the students that they have previously studied the Pythagorean Theorem, which will help find the relationships between the sides.
  4. The teacher should monitor students' progress on Desmos to identify problems or gaps in learning.
Assessment Strategies

Assessment Strategies

Once the students share their answers with the class, they can see three other students' answers for a comparison of the correctness of their work. The teacher can assess the students' answers in Desmos as well by checking the students' responses. The teacher should correct the students' mistakes or misunderstandings.

Variation Tips

Students could work in pairs to complete this activity. If students do not have access to a device, the activity could be done as a whole group activity. If using with a whole group, the teacher should have students write their answers on whiteboards or paper and check for mistakes. 

Background and Preparation

Background / Preparation

The teacher will need to ensure the classroom has the following:

1) internet connection (WiFi).

2) classroom set of computers, iPads, or smart devices. (If allowed students can use their own personal devices.)

Prior to the lesson, the teacher should be familiar with Desmos and should create a free class code for the activity. If the teacher does not have a Desmos account, he/she will need to create a free Desmos account. Prior to the lesson, the teacher may want to review the Pythagorean Theorem and altitude.

Digital Tools / Resources

https://teacher.desmos.com/activitybuilder/custom/5efdb520726e1a4b5dd64cbc

Approved Date

Owner (Author)

mrswhite
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