Unit Three: Continued Proofs - Transversals and Special Angles
Match the reasons with the statements. Complete the proof for Theorem 3-16 above, with the information given. Given: m∠1 = m∠2 Prove: l || m Plan: Same as Theorem 3-15 STATEMENTS: 1. m∠1 = m∠2 2. m∠1 = m∠3 3. m∠2 = m∠3 4. l||m REASONS: Substitution Given If corresponding angles are equal, then lines are parallel Vertical angles are equal
1. Given 2. Vertical angles are equal 3. Substitution 4. If corresponding angles are equal, then lines are parallel
Write the converse of this statement. If two angles are both obtuse, the two angles are equal. Converse:
If two angles are equal, then two angles are both obtuse.
Write the converse of this statement. If 2 angles are supplementary, then they are not equal. Converse:
If two angles are not equal, then they are supplementary.
Which of the following statements is the converse of the statement, "If each of two angles has a measure of 28 degrees, then the two angles are equal in measure"? If each of two angles does not have a measure of 28 degrees, then the two angles do not have equal measures. If each of two angles does not have a measure of 28 degrees, then the two angles have equal measures. If two angles have equal measures, then the measure of each is 28 degrees. If two angles do not have equal measures, then each of the two angles does not have a measure of 28 degrees.
If two angles have equal measures, then the measure of each is 28 degrees.
Write the converse of this statement. If 3 - 2x = 13, then x = -5. Converse:
If x= -5, then 3-2x=13.
Using the information given, select the statement that can deduce the line segments to be parallel. If there are none, then select none. When measure of angle 1 = measure of angle 6 Segment AB is parallel to Segment DC Segment AD is parallel to Segment BC none
None
Using the information given, select the statement that can deduce the line segments to be parallel. If there are none, then select none. When measure of angle 2 = measure of angle 3 Segment AB is parallel to Segment DC Segment AD is parallel to Segment BC none
None
Using the information given, select the statement that can deduce the line segments to be parallel. If there are none, then select none. When measure of angle 2 = measure of angle C Segment AB is parallel to Segment DC Segment AD is parallel to Segment BC none
None
Using the information given, select the statement that can deduce the line segments to be parallel. If there are none, then select none. When measure of angle 7 = measure of angle 1 Segment AB is parallel to Segment DC Segment AD is parallel to Segment BC none
None
Using the information given, select the statement that can deduce the line segments to be parallel. If there are none, then select none. When measure of angle 7 = measure of angle 4 Segment AB is parallel to Segment DC Segment AD is parallel to Segment BC none
None
Using the information given, select the statement that can deduce the line segments to be parallel. If there are none, then select none. When measure of angle 7 = measure of angle 8 Segment AB is parallel to Segment DC Segment AD is parallel to Segment BC none
None
Using the information given, select the statement that can deduce the line segments to be parallel. If there are none, then select none. When measure of angle 1 = measure of angle D Segment AB is parallel to Segment DC Segment AD is parallel to Segment BC none
Segment AB is parallel to Segment DC
Using the information given, select the statement that can deduce the line segments to be parallel. If there are none, then select none. When measure of angle 3 = measure of angle B Segment AB is parallel to Segment DC Segment AD is parallel to Segment BC none
Segment AD is parallel to Segment BC
Using the information given, select the statement that can deduce the line segments to be parallel. If there are none, then select none. When measure of angle 8 = measure of angle 4 Segment AB is parallel to Segment DC Segment AD is parallel to Segment BC none
Segment AD is parallel to Segment BC
Using the information given, select the statement that can deduce the line segments to be parallel. If there are none, then select none. When the measure of angle 1 = measure of angle B Segment AB is parallel to Segment DC Segment AD is parallel to Segment BC none
Segment AD is parallel to Segment BC
Using the information given, select the statement that can deduce the line segments to be parallel. If there are none, then select none. When measure of angle 2 = measure of angle 6 Segment AD is parallel to Segment BC Segment DC is parallel to Segment AB none
Segment DC is parallel to Segment AB
Using the information given, select the statement that can deduce the line segments to be parallel. If there are none, then select none. When measure of angle 7 = measure of angle 3 Segment AD is parallel to Segment BC Segment DC is parallel to Segment AB none
Segment DC is parallel to Segment AB
Which of the following statements could be true when a transversal crosses parallel lines? Select all that apply. Several congruent angles are formed. Vertical angles are formed. Complementary angles are formed. Supplementary angles are formed. Obtuse angles are formed.
Several congruent angles are formed. Vertical angles are formed. Supplementary angles are formed. Obtuse angles are formed.
