Question

1. the diagonal $overline{ac}$ is drawn in parallelogram $abcd$. which method can not be used to prove that $\triangle abccong\triangle cda$? draw it!!! 1) sss 2) sas 3) ssa 4) asa

in quadrilateral blue shown below, $overline{be}congoverline{ul}$. which information would be sufficient to prove quadrilateral blue is a parallelogram 1) $overline{bl}paralleloverline{eu}$ 2) $overline{lu}paralleloverline{be}$ 3) $overline{be}congoverline{bl}$ 4) $overline{lu}congoverline{eu}$

1. which of the following is true about a square? a) diagonals are not congruent. b) diagonals are perpendicular. c) only 1 pair of opposite sides parallel. d) consecutive angles are complementary.
2. given parallelogram to the right, a) what angle property would you use to solve for $x$? b) solve for $x$ and $y$.

Explanation:

Question 5:

Step1: Recall congruence - criteria

SSS (Side - Side - Side), SAS (Side - Angle - Side), ASA (Angle - Side - Angle) are valid congruence criteria for triangles. SSA (Side - Side - Angle) is not a valid congruence criterion as it does not always guarantee that two triangles are congruent. In parallelogram \(ABCD\) with diagonal \(AC\), \(\triangle ABC\) and \(\triangle CDA\) can be proven congruent by SSS (since \(AB = CD\), \(BC=DA\), \(AC = CA\)), SAS (e.g., \(AB = CD\), \(\angle BAC=\angle DCA\), \(AC = CA\)), and ASA (e.g., \(\angle BAC=\angle DCA\), \(AC = CA\), \(\angle ACB=\angle CAD\)).

Question 6:

Step1: Recall parallelogram - properties

One of the properties of a parallelogram is that if one pair of opposite sides is parallel and congruent. Given \(BE\cong UL\), if \(BL\parallel EU\), then quadrilateral \(BLUE\) is a parallelogram.

Question 7:

Step1: Recall square - properties

In a square:

• The diagonals are congruent.
• The diagonals are perpendicular.
• Both pairs of opposite sides are parallel.
• Consecutive angles are supplementary (\(180^{\circ}\)), not complementary (\(90^{\circ}\)). So the correct property is that the diagonals are perpendicular.

Question 8:

Step1: Identify angle - property for \(x\)

In a parallelogram, opposite angles are equal. So, to solve for \(x\), we use the property of opposite - angles equality.

Step2: Set up equations for \(x\) and \(y\)

Since opposite angles are equal, we have \(3x - 17=2x + 24\) (opposite - angle equality for \(x\) - related angles) and \(y + 58=5y-6\) (opposite - angle equality for \(y\) - related angles).

Step3: Solve for \(x\)

\[

$$\begin{align*} 3x-17&=2x + 24\\ 3x-2x&=24 + 17\\ x&=41 \end{align*}$$

\]

Step4: Solve for \(y\)

\[

$$\begin{align*} y + 58&=5y-6\\ 58+6&=5y-y\\ 64&=4y\\ y&=16 \end{align*}$$

\]

Answer:

1. 3) SSA
2. 1) \(\overline{BL}\parallel\overline{EU}\)
3. b) Diagonals are perpendicular.
4. a) Opposite - angles equality

b) \(x = 41\), \(y = 16\)