Question

1. Remember what we know about vertical angles and solve for x. (SHOW WORK)

2. Use the figure to answer the questions. (a) What additional information is needed to prove the triangles are congruent by SAS Postulate? Explain.
(b) What additional information is needed to prove the triangles are congruent by the HL Theorem? Explain. (SHOW WORK)

Answer 1

Ans 1.
`x= 7`

Ans 2.a.

`\overline {AC} \cong \overline {JL} \\\textrm{is the additional information required to prove the triangles are congruent by SAS postulate}`

Ans.2.b.

`\overline {BC} \cong \overline {KL} \\\textrm{is the additional information required to prove the triangles are congruent by the HL theorem}`

Explanation:

Solution:

1.

Vertically opposite angles are equal.

`\therefore (x+16) = (4x-5)\\\therefore (4x-x) = (16+5)\\\therefore (3x) = (21)\\\therefore x = 7`

2.a.

proof for Δ BAC ≅ ΔKJL by SAS postulate.

InΔ BAC and Δ KJL

BA ≅ KJ Given

∠ BAC ≅ ∠ KJL {measure each angle is 90}

`\overline{AC} \cong \overline{JL}\ \textrm{additional information require to prove the tangles are congruent by SAS postulate}\\\therefore \triangle BAC \cong \triangle KJL\ \textrm{By Side-Angle-Side postulate...PROVED}`

2.b.

proof for Δ BAC ≅ ΔKJL by HL theorem.

InΔ BAC and Δ KJL

BA ≅ KJ Given

∠ BAC ≅ ∠ KJL {measure each angle is 90}

`\overline{BC} \cong \overline{KL}\ \textrm{additional information require to prove the tangles are congruent by HL theorem}\\\therefore \triangle BAC \cong \triangle KJL\ \textrm{By Hypotenuse Leg Theorem......PROVED}`