Given: AB ≅ CD ∠EGC ≅ ∠CGB

Prove: ∠AGD is complementary to ∠EGC.

Proof:

StatementhReason

1. given

2. m∠EGB = 90°definition of perpendicular lines

3. ∠EGB = ∠EGC + ∠CGBangle addition

4. ∠EGC + ∠CGB = 90°Transitive Property of Equality

5. ∠EGC is complementary to ∠CGB. definition of complementary angles

6.What is the next step in the given proof? Choose the most logical approach.

A.

Statement: ∠EGC ≅ ∠AGD

Reason: Substitution Property of Equality

B.

Statement: ∠CGB ≅ ∠AGD

Reason: Vertical Angles Theorem

C.

Statement: ∠EGA and ∠EGB are supplementary.

Reason: Linear Pair Theorem

D.

Statement: ∠AGD and ∠DGB are supplementary.

Reason: Linear Pair Theorem

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.