Answer this carefully Part #1 - Find x, show your solution . Item 1-2 only Part ...

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September 2022 1 4 Report

Answer this carefully

Part #1 - Find x, show your solution . Item 1-2 only

Part #2 - Fill in the blank. Item 1-6

Part #3 - Answer A and B

Unhelpful answer will be reported

Answers & Comments

chirilu

$\large\textsf{PART 1. Find x.}$

$\textsf{Number 1:}$

x is a base angle of an isosceles triangle.
The other base angle is 73°.
Using the Isosceles Triangle Theorem,

$\qquad \qquad\qquad\red{\boxed{\tt x=73°}}$

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65° is a base angle of an isosceles triangle.
∠2 is a vertex angle.
Using the Isosceles Triangle Theorem,

$\qquad\tt 65+65+m\angle 2=180 \\ \\ \qquad\tt 65+65+8x - 6 = 180 \\ \\ \qquad\tt 124+8x=180 \\ \\ \qquad\tt 8x=180-124 \\ \\ \qquad\tt 8x=56 \\ \\ \qquad\tt \frac{8x}{8} = \frac{56}{8} \\ \\ \qquad\red{\boxed{\tt x=7}}$

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*The two-column proof is attached above.

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$\textsf{For A:}$

Answer: $\red{\tt \overline{LJ}\cong \overline{LM}, \overline{LK}\cong \overline{LK}}$ or

$\qquad\qquad$ $\red{\tt \overline{LJ}\cong \overline{LM}, \overline{JK}\cong \overline{MK}}$

Explanation:

☞ HL Congruence Theorem requires that the hypotenuse and a leg of the first right triangle is congruent to the corresponding hypotenuse and a leg of the second right triangle.

☞ Just as long as the hypotenuse of the two triangles are congruent, any of the two corresponding legs can suffice the HL Congruence Theorem.

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Answer: $\red{\tt LL\: Congruence\:Theorem}$

Explanation:

☞The LL Congruence Theorem requires that two corresponding legs of the two right triangles are congruent.

First corresponding legs: Given that K is the midpoint of JM, we can prove that JK≅MK by Definition of Midpoint.
Second corresponding legs: LK≅LK by Reflexive Property of Equality.

$>#CarryOnLearning <div class=$

12 votes Thanks 64

chirilu sorry nalate ang "bukas" ^^

chirilu you're welcome! :)

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