| {{ 'ml-lesson-number-slides' | message : article.intro.bblockCount }} |
| {{ 'ml-lesson-number-exercises' | message : article.intro.exerciseCount }} |
| {{ 'ml-lesson-time-estimation' | message }} |
Here are a few recommended readings before getting started with this lesson.
$≅$is used.
Consider different pairs of figures. Are they congruent figures or not?
There is also a type of transformation that creates an image that is not identical, but very similar to its preimage.
$∼$indicates that two figures are similar.
Congruent or Similar? | Relationship |
---|---|
Congruent | The corresponding sides and angles of the figures are congruent. |
Similar | The corresponding sides of the figures are proportional.
The corresponding angles of the figures are also congruent. |
Two polygons are similar if and only if both of the following two properties hold.
Consider a pair of similar polygons. Notice how both of these properties hold for these polygons.
It is given that the length of the first snowflake is $3$ millimeters. Since the snowflakes are congruent, the length of the second snowflake must also be $3$ millimeters.
The congruence of the snowflakes indicates that they are identical and have the same lengths and angle measures. That means the corresponding angle on the second snowflake has the same measure of $60_{∘}.$
Scale Factor |
A scale factor of two similar figures is the quotient of the measure of one figure and the measure of the other figure. |
The width of the larger frame is measured to be $5.6$ feet and the width of the smaller frame is $4.2$ feet.
To find the scale factor from the smaller frame to the larger one, divide $4.2$ by $5.6$ and simplify the quotient.Paulina goes on to enter The Room of Games! She notices beautifully crafted chess sets and playing cards. Their details are different sizes depending on the piece and card. The purpose of the room is clear to her — similarities and congruence in shapes are being displayed across various games.
Consider two similar figures. Using the given information, find the scale factor rounded to two decimal places or the length of either of the figures rounded to the closest integer.
Paulina entered the final room of the gallery. It is dedicated to congruent and similar figures in architecture. There is a model of an old castle with two towers with congruent shapes.
Notice that the roofs of the towers in front of the castle look like congruent triangles.