Lara and jerome are examining the triangles formed by a diagonal of a parallelogram.
lara believes a diagonal will always partition a parallelogram into two congruent triangles. she says that because the diagonal acts as a transversal between parallel lines, the asa congruence criteria is satisfied by the diagonal and two angles formed by the transversal. jerome believes a diagonal will always partition a parallelogram into two isosceles triangles. he says that because every parallelogram has two pairs of congruent opposite sides, each triangle formed will have a pair of congruent legs. whose reasoning is valid?

a. only lara's reasoning is valid.
b. neither lara's nor jerome's reasoning is valid.
c. only jerome's reasoning is valid.
d. both lara's and jerome's reasoning is valid

the two may have that, even a breakdown is probably offered

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°

what is

step-by-step explanation:

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm