fill in the blank with the appropriate word, phrase, or symbol to make a true statement.
1. similar figures have the same but not necessarily the same
2. the symbol means \is similar to\ and the symbol is the abbreviation for the word angle.
3. a drawing is an enlarged or reduced drawing that is similar to an actual object or place.
4. in similar triangles, corresponding are congruent and corresponding are in proportion.
5. to find a missing side length set up and solve a. put the measurements of the smaller figu on top and the bigger figure on the bottom.
learning goal # 1: i can identify the corresponding parts of similar figures.
example: the figures in each pair are similar ($ \triangle abc\sim\triangle xyz $).
$ \angle a $ corresponds with $ \angle $ _. ab matches with _.
$ \angle b $ matches with $ \angle $ _. ba corresponds with _.
$ \angle c $ corresponds with $ \angle $ _. bc matches with _.
practice problems
1. $ \triangle sit\sim\triangle dog $
first, label $ \angle d, \angle o, \&\angle g $ on the small triangle. then, fill in the blanks below:
$ \angle d $ corresponds with $ \angle $ _. do matches with _.
$ \angle o $ matches with $ \angle $ _. it corresponds with _.
$ \angle g $ corresponds with $ \angle $ _. st matches with _.
suppose $ \angle s = 25^{\circ} $, what is the measure of $ \angle d $?
2. $ \triangle hot\sim\triangle pig $
$ \angle h $ corresponds with $ \angle $ _. pi matches with _.
$ \angle o $ matches with $ \angle $ _. ig corresponds with _.
$ \angle t $ corresponds with $ \angle $ _. gp matches with _.

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# Brief Explanations:
For similar figures, by definition, corresponding angles are congruent and corresponding sides are in proportion. When two triangles are similar (denoted by the symbol ~), the order of the letters in the triangle names gives the correspondence of their parts.

For example, in $\triangle ABC\sim\triangle XYZ$:
- The first - letter $A$ of $\triangle ABC$ corresponds to the first - letter $X$ of $\triangle XYZ$ for angles and sides.
- The second - letter $B$ of $\triangle ABC$ corresponds to the second - letter $Y$ of $\triangle XYZ$.
- The third - letter $C$ of $\triangle ABC$ corresponds to the third - letter $Z$ of $\triangle XYZ$.

In $\triangle SIT\sim\triangle DOG$:
- Since the order is $S - I - T$ and $D - O - G$, $\angle D$ (first letter of $\triangle DOG$) corresponds to $\angle S$ (first letter of $\triangle SIT$), $\angle O$ (second letter of $\triangle DOG$) corresponds to $\angle I$ (second letter of $\triangle SIT$), $\angle G$ (third letter of $\triangle DOG$) corresponds to $\angle T$ (third letter of $\triangle SIT$).
- For sides, $DO$ (first - second letters of $\triangle DOG$) corresponds to $SI$ (first - second letters of $\triangle SIT$), $IT$ (second - third letters of $\triangle SIT$) corresponds to $OG$ (second - third letters of $\triangle DOG$), $ST$ (first - third letters of $\triangle SIT$) corresponds to $DG$ (first - third letters of $\triangle DOG$). And since $\angle S=\angle D$ (corresponding angles of similar triangles), if $\angle S = 25^{\circ}$, then $\angle D=25^{\circ}$.

In $\triangle HOT\sim\triangle PIG$:
- $\angle H$ (first letter of $\triangle HOT$) corresponds to $\angle P$ (first letter of $\triangle PIG$), $\angle O$ (second letter of $\triangle HOT$) corresponds to $\angle I$ (second letter of $\triangle PIG$), $\angle T$ (third letter of $\triangle HOT$) corresponds to $\angle G$ (third letter of $\triangle PIG$).
- For sides, $PI$ (first - second letters of $\triangle PIG$) corresponds to $HO$ (first - second letters of $\triangle HOT$), $IG$ (second - third letters of $\triangle PIG$) corresponds to $OT$ (second - third letters of $\triangle HOT$), $GP$ (third - first letters of $\triangle PIG$) corresponds to $TH$ (third - first letters of $\triangle HOT$).

For the initial fill - in - the - blank questions:
1. Similar figures have the same **shape** but not necessarily the same **size**.
2. The symbol **$\sim$** means "is similar to" and the symbol **$\angle$** is the abbreviation for the word angle.
3. A **scale** drawing is an enlarged or reduced drawing that is similar to an actual object or place.
4. In similar triangles, corresponding **angles** are congruent and corresponding **sides** are in proportion.
5. To find a missing side length set up and solve a **proportion**. Put the measurements of the smaller figure on top and the bigger figure on the bottom.

For the example $\triangle ABC\sim\triangle XYZ$:
- $\angle A$ corresponds with $\angle X$, $AB$ matches with $XY$.
- $\angle B$ matches with $\angle Y$, $BA$ corresponds with $YX$.
- $\angle C$ corresponds with $\angle Z$, $BC$ matches with $YZ$.

# Answer:
1. shape; size
2. $\sim$; $\angle$
3. scale
4. angles; sides
5. proportion

Example:
- $\angle A$ corresponds with $\angle X$, $AB$ matches with $XY$
- $\angle B$ matches with $\angle Y$, $BA$ corresponds with $YX$
- $\angle C$ corresponds with $\angle Z$, $BC$ matches with $YZ$

Practice Problem 1 ($\triangle SIT\sim\triangle DOG$):
- $\angle D$ corresponds with $\angle S$, $DO$ matches with $SI$
- $\angle O$ matches with $\angle I$, $IT$ corresponds with $OG$
- $\angle G$ corresponds with $\angle T$, $ST$ matches with $DG$
- $\angle D = 25^{\circ}$

Practice Problem 2 ($\triangle HOT\sim\triangle PIG$):
- $\angle H$ corresponds with $\angle P$, $PI$ matches with $HO$
- $\angle O$ matches with $\angle I$, $IG$ corresponds with $OT$
- $\angle T$ corresponds with $\angle G$, $GP$ matches with $TH$

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