Nesting BotTally Crew · numbers, fractions, measurement and shapes

Clockwork nesting dolls, the same shape at every size: proportions, similar figures and congruent triangles.

Proportion and Similar Figures

Proportions, similar figures and congruent triangles. In MathBound, the free Algebra I adventure game, Nesting Bot asks these problems, and the only way past is to solve them.

Part of Solving Linear Equations: chapter 2 of the standard course.

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10 questions, no sign-up, nothing saved. Climbs from the basics to harder questions.

What you will practice

Solve Proportions. Solve a basic proportion consisting of two single rational expressions.
Proportion Applications. Translate and solve a word problem using a proportion by carefully matching units in the numerator and denominator.
Similar Figures. Solve for missing side lengths of similar triangles by setting up a proportion of corresponding sides.

Worked examples

Made by the game’s own question engine. Try each one, then open its steps.

Example 1 · Solve Proportions

Cross-multiplying

\frac{x}{27} = \frac{4}{9}

gives

which

equation?

$27 x = 4 \cdot 9$
$9 x = 4 + 27$
$4 x = 9 \cdot 27$
$9 x = 4 \cdot 27$

Show the worked steps

$Cross-multiplying$ $sets$ $the$ $product$ $of$ $each$ $diagonal$ $equal:$ $x$ $times$ $9,$ $and$ $4$ $times$ $27 .$
$9 x = 4 \cdot 27,$ $so$ $x = 12 .$

Answer: $9 x = 4 \cdot 27$

Example 2 · Proportion Applications

A

car

uses

6

gallons

of

gas

to

drive

210

miles.

How

many

miles

can

it

drive

on

24

gallons?

$0.686$ $miles$
$5040$ $miles$
$840$ $miles$
$228$ $miles$

Show the worked steps

$\frac{6}{210} = \frac{24}{x},$ $gallons$ $over$ $miles$ $on$ $both$ $sides.$
$6 x = 5040,$ $so$ $x = 840$ $miles.$

Answer: $840$ $miles$

Example 3 · Similar Figures

Triangle

ABC

is

similar

to

triangle

XYZ.

A B = 15, B C = 6

and

X Y = 5 .

Find

Y Z .

$18$
$6$
$10$
$2$

Show the worked steps

$Corresponding$ $sides$ $are$ $in$ $proportion:$ $\frac{A B}{X Y} = \frac{B C}{Y Z} .$
$\frac{15}{5} = \frac{6}{Y Z},$ $so$ $Y Z = 2 .$

Answer: $2$

Where it is in your textbook

Textbook	Lessons
Standard course	2.6
Big Ideas Math Algebra 1 (2022)	1.3
CPM Core Connections Algebra	5.1.2
Glencoe Algebra 1	0-6, 2-6, 10-6
Holt McDougal Larson Algebra 1	2.6, 2.7
OpenStax Elementary Algebra 2e	8.7
Pearson Algebra 1 Common Core	2-7, 2-8, 10-6
Reveal Algebra 1	2-6

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