Problem 2 Constructing Congruent Angles

Construct an angle congruent to a given angle.

Given: ∠ A angle eh

Construct: ∠ S angle s  so that ∠ S ≅ ∠ A angle s approximately equal to angle eh

• Step 1

  Draw a ray with endpoint S.

• 

• Step 2

  With the compass point on vertex A, draw an arc that intersects the sides of ∠ A . angle eh .  Label the points of intersection B and C.

  

  Think

  Why do you need points like B and C?

  B and C are reference points on the original angle. You can construct a congruent angle by locating corresponding points R and T on your new angle.

• Step 3

  With the same compass setting, put the compass point on point S. Draw an arc and label its point of intersection with the ray as R.

  

• Step 4

  Open the compass to the length BC. Keeping the same compass setting, put the compass point on R. Draw an arc to locate point T.

  

• Step 5

  Draw S T → . s t vector , .

  ∠ S ≅ ∠ A angle s approximately equal to angle eh

  

✓ Got It?

2. 1. Construct ∠ F angle f  so that m ∠ F = 2 m ∠ B . m angle , f equals 2 m , angle b .

   2. Reasoning How is constructing a congruent angle similar to constructing a congruent segment?

      

Dynamic Activity

Constructing Congruent Segments and Angles