given: angle 1 is congruent to angle 2, angle measure 1=120
prove: angle measure 3=120
We do not see the figure, so do not know if angles 1 or 2 are interior or exterior angles of a triangle, or another polygon.
Please post remaining information or description.
To prove that angle measure 3 is also 120 degrees, we can use the fact that angle 1 is congruent to angle 2.
First, we need to establish some definitions:
- Angle 1 is congruent to angle 2 implies that angle 1 and angle 2 have the same measure.
- Let angle 3 be the angle we want to prove as congruent to angle 1 and angle 2.
Now, let's proceed with the proof:
Step 1: Given that angle 1 is congruent to angle 2, we know that angle 1 = angle 2. (Given)
Step 2: We are given the measure of angle 1 as 120 degrees. Therefore, angle 1 = 120 degrees. (Given)
Step 3: Since angle 1 = angle 2, we can substitute angle 2 with angle 1 in any equation involving angle 2.
Step 4: Substituting angle 2 with angle 1 in angle 1 = angle 2, we get angle 1 = angle 1.
Step 5: Using the reflexive property of congruence, we know that any angle is congruent to itself. Therefore, angle 1 is congruent to angle 1.
Step 6: By the transitive property of congruence, if angle 1 is congruent to angle 1 and angle 1 is congruent to angle 2, then angle 1 is congruent to angle 2.
Step 7: Applying the transitive property again, if angle 1 is congruent to angle 2 and angle 1 is 120 degrees, then angle 2 is also 120 degrees.
Step 8: Since angle 3 is congruent to angle 2 (as we want to prove angle measure 3 = 120), angle 3 must also be 120 degrees.
Therefore, we have proven that angle measure 3 is 120 degrees.
To prove that angle measure 3 is also 120 degrees, we need to use the given information that angle 1 is congruent to angle 2, and angle measure 1 is 120 degrees.
Here's the step-by-step explanation:
Step 1: Write down the given information:
Angle 1 is congruent to angle 2.
Angle measure 1 = 120 degrees.
Step 2: Use the definition of congruent angles:
Since angle 1 is congruent to angle 2, we can write: Angle 1 ≅ Angle 2.
Step 3: Apply the Transitive Property:
By the Transitive Property of congruence, if angle 1 is congruent to angle 2, and angle 1 has a measure of 120 degrees, then angle 2 also has a measure of 120 degrees.
This can be written as: Angle 2 = 120 degrees.
Step 4: Use the property of vertical angles:
Angle 3 is a vertical angle to angle 2, which means they share the same measure. Therefore, angle 3 should also have a measure of 120 degrees.
Step 5: Write the proof:
Based on the given information and the properties of congruent angles and vertical angles, we can conclude that angle measure 3 is also 120 degrees. This can be written as: Angle measure 3 = 120 degrees.
Overall, angle measure 3 is proven to be 120 degrees through the use of congruent angles and the properties of vertical angles.