Answer:
X=-4
Step-by-step explanation:
16x^2+9=5
- 9 -9
16x^2= -4
16/-4 =
-4
<span>Question 1
Given: m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100°
To prove that: △HKJ ~ △LNP
Statement Reason
1. m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100° 1. given
2. m∠H + m∠J + m∠K = 180° 2. ?
3. 30° + 50° + m∠K = 180° 3. substitution property
4. 80° + m∠K = 180° 4. addition
5. m∠K = 100° 5. subtraction property of equality
6. m∠J = m∠P; m∠K = m∠N 6. substitution
7. ∠J ≅ ∠P; ∠K ≅ ∠N 7. if angles are equal then they are congruent
8. △HKJ ~ △LNP 8. AA similarity theorem
The reason that is missing in step 2 is triangle angle sum theorem.
</span>The triangle angle sum theorem states that t<span>he sum of the measures of the interior angles of a triangle is 180°.
</span>Question 2
<span>Given that △ABC is an isosceles triangle with legs AB and AC and △AYX is also an isosceles triangle with legs AY and AX.
To prove that △ABC ~ △AYX.
Statements Reasons
1. △ABC is isosceles with legs AB and AC;
△AYX is also isosceles with legs AY and AX. 1. given
2. AB ≅ AC and AY ≅ AX 2. definition of isosceles triangle
3. AB = AC and AY = AX 3. definition of congruency
4. AY • AC = AX • AC 4. multiplication property of equality
5. AY • AC = AX • AB 5. substitution property of equality
6. AY </span><span>• AC / AB = AX 6. division property of equality
7. AY/AB = AX/AC 7. division property of equality
</span><span>8. ? 8. ?
9. △ABC ~ △AYX 9. SAS similarity theorem
The statement and reason missing in the proof are ∠A ≅ ∠A; reflexive property</span>
<span>SAS Similarity or Side-Angle-Side similarity states that when two triangles have corresponding angles that are congruent and corresponding sides with identical ratios, then the triangles are similar.</span>
<span>Question 3 -
Given that line RS intersects triangle BCD at two points and is parallel to segment DC.
The statements thet are correct is △BCD is similar to △BSR.</span>
Step-by-step explanation:
option A is the correct answer
Answer:
the answer is in the pic so like yea hope that helps
