Similar Right Triangles
(Geometric Mean)
Today you will need:
Grab a warm-up from the wooden desk and get started!
Goals:
Warm-up #1
Warm-up #2
Warm-up #1
Warm-up #2
Classify each solid. Highlight the base(s)!
Rectangular Pyramid
Cone
Triangular Prism
Hexagonal Pyramid
Cylinder
Rectangular Prism
Trapezoidal Prism
Rectangular Pyramid
Pentagonal Prism
Triangular Pyramid
Triangular Prism
Sphere
Similar Right Triangles
100
x
x
36
64
Can you find the missing side lengths?
Similar Right Triangles
| Short Leg | Long Leg | Hypotenuse |
Small Triangle | | | |
Medium Triangle | | | |
Large Triangle | | | |
Example: Find the geometric mean of 4 and 36.
Similar Right Triangles
Write proportionality statements to relate the sides of the similar right triangles shown.
Similar Right Triangles
| Short Leg | Long Leg | Hypotenuse |
Small Triangle | | | |
Medium Triangle | | | |
Large Triangle | | | |
Find the geometric mean of two numbers
Answers should be in simplest radical form.
Find the geometric mean of 8 and 18. | Find the geometric mean of 20 and 25 | 15 is the geometric mean of 25, what is the other number? |
Find the geometric mean of 3 and 7. | 32 is the geometric mean of 16 and what other number? | Find the geometric mean of 12 and 8. |
Independent Practice:
Delta Math G13: Triangles
Q3 Skill & Drill (due 3/18/2020)
Resources
Mod 5 Standards
G.SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor:�a. A dilation takes a line not passing through the center of the dilation to a parallel line and leaves a line passing through the center unchanged.�b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
G.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
G.SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to justify relationships in geometric figures that can be decomposed into triangles.
G.SRT.8 Solve problems involving right triangles�a. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems if one of the two acute angles and a side length is given.
G.SRT.4 Prove and apply theorems about triangles. Theorems include but are not restricted to the following: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to justify relationships in geometric figures that can be decomposed into triangles.
Warm-up #2
Directions: The black triangle is a right triangle with legs 8 and 6. The vertices are at the points (0,0), (0,8), and (6,0). The red line segment is perpendicular to hypotenuse. Find the length of the red line segment.
Warm-up #2
Directions: The black triangle is a right triangle with legs 8 and 6. The vertices are at the points (0,0), (0,8), and (6,0). The red line segment is perpendicular to hypotenuse. Find the length of the red line segment.
Hints:
https://www.openmiddle.com/finding-the-length-of-a-right-triangles-altitude/
Investigation with construction tools! :-)