Triangles Introduction

What is the minimum number of acute angles in a triangle?

• 2

• 3

• 1

• 0

Every exterior angle of a triangle forms __________________ with an interior angle

• a linear pair

• vertical angles

• complementary angles

• a triangle

Given the triangle sum theorem, what relationship do the acute angles of a right triangle have?

• complementary

• supplementary

• linear pair

• congruence

Tags

CCSS.7.G.B.5

The measure of an exterior angle of a triangle is equal to _________________.

• The sum of the measures of the remote interior angles.

• The sum of the measures of the interior angles.

• The measure of its adjacent interior angle.

• 360

Tags

CCSS.HSG.CO.C.10

If two triangles are congruent, then every part of one triangle will have a corresponding part in the other triangle to which it is congruent. We say that "Corresponding Parts of Congruent Triangles are Congruent." What would be a great way to abbreviate this?

• CPCTC

• CTCPC

• PCTCC

• TCPCP

Since parts of congruent triangles have corresponding parts, we have to make sure that, when we name congruent triangles, the angles that correspond to one another line up in the names.  Given how the angles and sides are marked as congruent, which triangle is  $\Delta BCA$  congruent to?

•  $\Delta EFD$  

•  $\Delta DEF$  

•  $\Delta FED$  

•  $\Delta DFE$  

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.CO.C.10

In the figure, which part of  $\Delta DEF$  is a corresponding part to  $\overline{AC}$  ?

•  $\overline{DF}$  

•  $\angle D$  

•  $\overline{DE}$  

•  $\angle F$  

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.SRT.B.5

Guess what! There's a transitive property of congruence for triangles! If  $\Delta PQR\cong\Delta STU$  and  $\Delta PQR\cong\Delta XYZ$  , what must be true?

•  $\Delta STU\cong\Delta XYZ$  

•  $\Delta PQR\cong\Delta UTS$  

•  $\Delta PQR\cong\Delta ZYX$  

•  $\Delta STU\cong\Delta ZYX$  

In triangles, the size of an angle determines how long the side opposite it becomes (big angles are opposite long sides. Don't worry, we'll prove this). The converse is also true. A long side means the angle opposite must be bigger. In an isosceles triangle, we have at least two sides that are congruent. What does this tell us?

• The angles opposite those sides must be congruent.

• The angles adjacent to those sides must be congruent

• The angles exterior to those sides must be congruent

• The angles formed by those sides must be congruent.

We know that equilateral triangles are just special isosceles triangles. What does the base angles theorem tell us must be another property of an equilateral triangle?

• It's also equiangular (it has 3 congruent angles)

• Each of its angles measures $90\degree$ .

• It also has exactly two congruent angles.

• All of its sides are congruent.