Given: ab ≅ cd
∠egc ≅ ∠cgb
prove: ∠agd is complementary to ∠egc.
proof:
statementh reason
1. given
2. m∠egb = 90° definition of perpendicular lines
3. ∠egb = ∠egc + ∠cgb angle 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

y < -3

step-by-step explanation:

-3y - 2 > 7

-3y -2 + 2 > 7+2

-3y > 9

-3y/-3 < 9/-3   (change the inequality sign when multiplying or dividing by a negative number)

y < -3

26 is 33.33% of 78

step-by-step explanation:

26 is what percent of 78?

26 is p% of 78

equation: y = p% * x

solving our equation for p

p% = y/x

p% = 26/78

p = 0.3333

convert decimal to percent:

p% = 0.3333 * 100 = 33.33%

m∠5 + m∠3 = m∠1   is true.

m∠5 + m∠6 = 180 is true

m∠2 +m∠3 = m∠6   is true

m∠2 +m∠3 +m∠5 = 180   is true

step-by-step explanation:

assume that you have 3 different side lengths.   apply the pythagorean theorem here:   square each of the two shortest sides; call them a and b, so that their squares are a² and b².   also square the longest side, calling the result c².

now, if a² + b² = c² is true, the triangle is a right triangle; otherwise it is not a right triangle.