Question

1. using the figure below, if p is the circumcenter of △abc, what is the length of ba? a. 38 b. 32 c. 64 d. impossible to find 11. in rectangle fghi, diagonals fh and gi intersect at e. ie = 3x + 4 and eg = 5x - 6. what is the length of fh? a. 19 units b. 38 units c. 5 units d. 10 units 12. all parallelograms have: a. opposite angles that are congruent b. 4 congruent sides c. opposite angles that are supplementary d. diagonals that are congruent 13. all parallelograms have: a. consecutive angles that are congruent b. diagonals that bisect each other c. opposite angles measure 90 degrees d. 4 congruent angles 14. based on the given information, what can you conclude, and why? given:∠h≅∠l, hj≅jl, △hij≅△lkj by a. saa b. sas c. ssa d. asa

Explanation:

Step1: Recall circum - center property

The circum - center of a triangle is equidistant from the vertices of the triangle. But the given figure and information do not provide enough data to find the length of BA. So for question 10, the answer is D.

Step2: Use rectangle diagonal property

In a rectangle, the diagonals are equal and bisect each other. So \(IE = EG\). Set up the equation \(3x + 4=5x - 6\).
\[

$$\begin{align*} 3x+4&=5x - 6\\ 4 + 6&=5x-3x\\ 10&=2x\\ x& = 5 \end{align*}$$

\]

Step3: Find the length of a diagonal segment

Substitute \(x = 5\) into the expression for \(IE\): \(IE=3x + 4=3\times5+4=15 + 4=19\).

Step4: Calculate the length of the diagonal

Since the diagonals of a rectangle are equal and bisect each other, \(FH = 2\times IE\). So \(FH=2\times19 = 38\). For question 11, the answer is B.

Step5: Recall parallelogram angle and side properties

For question 12, in a parallelogram, opposite angles are congruent. So the answer is A.

Step6: Recall parallelogram diagonal property

For question 13, in a parallelogram, the diagonals bisect each other. So the answer is B.

Step7: Recall triangle congruence postulates

For question 14, we are given two angles and a non - included side. The SAA (or AAS) postulate states that if two angles and a non - included side of one triangle are congruent to the corresponding two angles and non - included side of another triangle, then the two triangles are congruent. So the answer is A.

Answer:

1. D. Impossible to find
2. B. 38 units
3. A. Opposite angles that are congruent
4. B. Diagonals that bisect each other
5. A. SAA