Match the reasons with the statements given. given: < 1=< 2, < 5=< 6. prove: mq=mp
1. < 3, < 5 are supplementary and < 4, < 6 are supplementary
2. < 5=< 6 and < 1=< 2 (given)
3. < 3=< 4
4. mn=mn
5. triangle mnq congruent to triangle mnp
6. mq=mp

-asa
-exterior sides in opposite rays
-given
-supplements to = angles
-cpcte
-reflexive

me!

1.<3,<5 are supplementary and <4, <6 are supplementary -Exterior sides in opposite rays

2. <5=<6 and <1=<2 - Given

3. <3=<4 - Supplements to = angles

4. MN=MN - Reflexive

5. Triangle MNQ congruent to Triangle MNP - ASA

6. MQ=MP - CPCTE

Step-by-step explanation:

Its given that <1=<2, <5=<6

At point N, pairs <3,<5 and <4,<6 are supplementary angles as adjacent angles whose exterior sides are always supplementary,

hence ∠3+∠5=180° and ∠4+∠6=180°

⇒∠3=180°-∠5 and ∠4=180°-∠6

but its given that ∠5=∠6,

⇒∠3=∠4=180°-∠5

hence ∠3=∠4 (they supplement to equal angles)

Also from the figure we can see that MN=MN (reflexive relation)

Therefore, ΔMNQ≅ΔMNP (by ASA criteria) as

therefore, MQ=MP (congruent parts of congruent triangles are equal,i.e. CPCTE)

Step-by-step explanation:

1.<3,<5 are supplementary and <4, <6 are supplementary -Exterior sides in opposite rays

2. <5=<6 and <1=<2 - Given

3. <3=<4 - Supplements to = angles

4. MN=MN - Reflexive

5. Triangle MNQ congruent to Triangle MNP - ASA

6. MQ=MP - CPCTE

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