ANGLES - Geometry Jargon

ANGLES - Geometry Jargon

Geometric Symbols & Concepts

TODAY'S TOPICS

• Naming Sides

• Corresponding Parts

• Congruent Shapes

• Congruent Clues

• Similar Shapes

• Equilateral Triangles

• Isosceles Triangles

SIDES vs ANGLES

• ANGLES: are named using 1 or 3 letters

• EXAMPLE 1:   $\angle R\ =\ 82\degree$  

• EXAMPLE 2:   $\angle QRS\ =\ 82\degree$  

• SIDES: are named using  2 letters

• EXAMPLE 1:   $\overline{QR}$  =  $\overline{RQ}$  

• EXAMPLE 2:   $\overline{RS}$  =  $\overline{SR}$  

Multiple Choice

1)  In polygon $ABCD$ , which side does not exist?

•  $\overline{AB}$  

•  $\overline{BC}$  

•  $\overline{CA}$  

•  $\overline{DA}$  

• They all exist in the polygon.

CORRESPONDING

• "Matching" angles or sides

• WITHIN SAME IMAGE:  Use locations to find matching parts ("Both are top-left")

• SHAPES:  Always line up the names to find matching parts (ignore the picture)
  

• EX:   $\Delta ABC$  vs

          $\Delta GHI$  

•  $\angle A$  corresponds to  $\angle G$  

•  $\angle B$  corresponds to  $\angle H$  

•  $\overline{AC}$  corresponds to  $\overline{GI}$  

Fill in the Blanks

2) If trapezoid HIJK is an exact copy of trapezoid EFGH, then

 $\angle J$  corresponds to  $\angle_{ }$  

.

Fill in the Blanks

3)  $\Delta TUV$  was copied to create  $\Delta WXY$ .  Therefore,

 $\overline{WY}$  corresponds to  $\overline{??}$ .

CONGRUENT SHAPES

• All Corresponding Angles are equal

• All Corresponding Sides are equal

• Essentially...same shape, same size

• The shape may be turned or flipped.

CONGRUENT CLUES

• Equal sides are shown with "tic marks"

• EXAMPLE:

   $\overline{AC}\ =\ \overline{DF}$  since both have 3 marks

• Equal angles are shown with "arches"

• EXAMPLE: 
   $\angle C=\angle F$  since both have 2 arches

• The congruent symbol:   $\cong$  

•  $\Delta ABC\cong\Delta DEF$   means all their matching parts are equal (twin shapes)

Fill in the Blanks

4) $\Delta FGH$ and  $\Delta PQR$  are congruent right triangles.  If   $\angle F=20\degree$  $\angle G=70\degree$  and $\angle H=90\degree$ then find $m\angle Q$ . 

Fill in the Blanks

5) $\Delta FGH$ and  $\Delta PQR$  are congruent scalene triangles.  If   $FG=5\ inches$  $GH=3\ inches$  and $FH=7\ inches$ then $\overline{QR}$ must be

inches. 

EQUILATERAL TRIANGLE

Three equal sides, three equal angles ( $60\degree$  each)

Multiple Choice

6) All equilateral triangles are congruent.

• TRUE

• FALSE

ISOSCELES TRIANGLE

Two equal sides, two equal angles (many options)

Multiple Choice

7) All isosceles triangles are congruent.

 

• TRUE

• FALSE

SIMILAR SHAPES - Part I

• All Corresponding Angles are equal

• All Corresponding Sides are proportional (times the same amount)

• Essentially...same shape, different size.

• THINK: Giant or Miniature version

• CAN BE: bigger or smaller

• CANNOT BE: fatter or thinner

Multiple Choice

8) All equilateral triangles are similar since the angles are always $60\degree$  

 

• TRUE

• FALSE

Multiple Choice

9) All isosceles triangles are similar since they have a lot in common.

 

• TRUE

• FALSE

SIMILAR SHAPES - Part II

• Similar symbol:  $\approx$  

•  $ABCD\approx WXYZ$  means one is a "giant" version of the other

• The sides grew (times the same factor)

• The angles did not change

Multiple Choice

10) If two shapes are similar then they will look almost identical, but the _______may be several times larger.

• sides

• angles

• muscles