Question

try this video extra example 3 for 3a - using the vertical angles congruence theorem

1. use the diagram and the given angle measure to find the other three angle measures.

m∠3 = 128°

1. use the reason bank along with the given paragraph proof to write a two - column proof.

given: ∠1 ≅ ∠2
prove: ∠1 ≅ ∠3
paragraph proof
we are given ∠1 ≅ ∠2. by the definition of vertical angles, ∠2 and ∠3 are vertical angles. therefore, ∠2 ≅ ∠3, by the vertical angles congruence theorem. so, by the transitive property of angle congruence, ∠1 ≅ ∠3.
two - column proof

statements	reasons
2. ∠2 and ∠3 are vertical angles.	2.
3. ∠2 ≅ ∠3	3.
4. ∠1 ≅ ∠3	4.

reasons bank
transitive property of angle congruence
vertical angles congruence theorem
definition of vertical angles
given

Explanation:

Step1: Solve problem 2, find ∠1 measure

Vertical angles are congruent, so $m\angle1 = m\angle3 = 128^\circ$

Step2: Solve problem 2, find ∠2 measure

Linear pair sums to $180^\circ$, so $m\angle2 = 180^\circ - 128^\circ = 52^\circ$

Step3: Solve problem 2, find ∠4 measure

Vertical angles are congruent, so $m\angle4 = m\angle2 = 52^\circ$

Step4: Fill problem 3, reason 1

Match given statement to reason: Given

Step5: Fill problem 3, reason 2

Match vertical angle definition: Definition of Vertical Angles

Step6: Fill problem 3, reason 3

Match vertical angle congruence theorem: Vertical Angles Congruence Theorem

Step7: Fill problem 3, reason 4

Match transitive property: Transitive Property of Angle Congruence

Answer:

Problem 2:

$m\angle1 = 128^\circ$, $m\angle2 = 52^\circ$, $m\angle4 = 52^\circ$

Problem 3 (Completed Two-Column Proof):

STATEMENTS	REASONS
2. $\angle2$ and $\angle3$ are vertical angles.	2. Definition of Vertical Angles
3. $\angle2 \cong \angle3$	3. Vertical Angles Congruence Theorem
4. $\angle1 \cong \angle3$	4. Transitive Property of Angle Congruence