Choose the pair of vertical lines

choose all that apply

a. < b and < c
b. < b and < d
c. < a and < c
d. < a and < b

question 2.

a rigid transformation results in a figure that is twice as large as the original

a. true
b. false

question 3.
which of the following are congruent triangles facts sufficient to prove triangles congruent?

a. aaa (angle-angle-angle)
b. sas (side-angle-side)
c. ha (hypotenuse angle)
d. sss (side-side-side)
e. hl (hypotenuse leg)
f. aas (angle-angle-side)
g. als (angle-leg-side)
h. asa (angle-side-angle)

question 4.
two lines that intersect and form right angles are called

a. infinity
b. segmented
c. perpendicular
d. parallel

1. The pair of vertical angles from the attached diagram are:

<B and <D (OPTION B)

<A and <C (OPTION C)

Vertical angles (which are also known as opposite angles) are a pair of non-adjacent angles which are formed by the intersection of two lines. A pair of vertical angles have an equal measure.

2. False

A rigid transformation DOES NOT result in a figure that is twice as large as the original. A rigid transformation preserves length, therefore it results in a figure that is just as large as the original. Rigid transformation is also called an isometry.

3. The following options (B, D, E, F and H) are the congruent triangles facts that are sufficient to prove triangles congruent
b. SAS (side-angle-side)
d. SSS (side-side-side)
e. HL (hypotenuse leg)
f. AAS (angle-angle-side)
h. ASA (angle-side-angle)

4. Perpendicular lines is the term used in elementary geometry to describe two lines that intersect and form right angles (90 degrees). Perpendicularity is a symmetric property, that is, if line A is perpendicular to line B, then line B is also perpendicular to line A.

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)