Nesting BotTally Crew · numbers, fractions, measurement and shapes

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

Triangle Congruence

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 More topics: taught by some textbooks beyond the usual course.

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

What you will practice

Congruence Criteria. Name the criterion (SSS, SAS, ASA, AAS) that the marked parts of two triangles show.
Corresponding Parts. Name the side or angle that corresponds in a congruence statement.
Constructions. Tell what a compass-and-straightedge construction makes.

Worked examples

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

Example 1 · Congruence Criteria

In

two

triangles,

three

sides

of

one

are

equal

to

the

matching

parts

of

the

other.

Which

criterion

proves

the

triangles

congruent?

$AAS$
$SSS$
$SAS$
$ASA$

Show the worked steps

$S$ $stands$ $for$ $a$ $pair$ $of$ $matching$ $sides,$ $A$ $for$ $a$ $pair$ $of$ $matching$ $angles,$ $in$ $order$ $around$ $the$ $triangle.$
$All$ $three$ $pairs$ $of$ $sides$ $match:$ $SSS.$

Answer: $SSS$

Example 2 · Corresponding Parts

△ P QR ≅ △ Z Y X .

Which

side

corresponds

to

P Q ?

$Y X$
$Z Y$
$QR$
$Z X$

Show the worked steps

$Matching$ $letters$ $sit$ $in$ $the$ $same$ $places:$ $P$ $matches$ $Z$ $and$ $Q$ $matches$ $Y .$
$So$ $P Q$ $corresponds$ $to$ $Z Y .$

Answer: $Z Y$

Example 3 · Constructions

Which

construction

gives

a

ray

that

cuts

an

angle

into

two

equal

angles ?

$the$ $perpendicular$ $bisector$ $of$ $a$ $segment$
$the$ $bisector$ $of$ $an$ $angle$
$an$ $equilateral$ $triangle$
$a$ $copy$ $of$ $a$ $segment$

Show the worked steps

$An$ $arc$ $centered$ $at$ $the$ $vertex$ $of$ $an$ $angle$ $crosses$ $both$ $of$ $its$ $sides.$ $Equal$ $arcs$ $from$ $those$ $two$ $crossings$ $meet$ $inside$ $the$ $angle,$ $and$ $a$ $ray$ $is$ $drawn$ $from$ $the$ $vertex$ $through$ $that$ $point.$
$So$ $the$ $bisector$ $of$ $an$ $angle$ $gives$ $a$ $ray$ $that$ $cuts$ $an$ $angle$ $into$ $two$ $equal$ $angles .$

Answer: $the$ $bisector$ $of$ $an$ $angle$

Where it is in your textbook

Textbook	Lessons
MVP Mathematics I (Integrated Math 1)	7.1, 7.2, 7.3, 7.4, 7.5, 7.6

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