Question

PLEASEEEE HELPPP!!!!!

Answer 1

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.
The triangle angle sum theorem states that the sum of the measures of the interior angles of a triangle is 180°.

Question 2
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 • AC / AB = AX                                              6. division property of equality
7. AY/AB = AX/AC                                                  7. division property of equality
8. ?                                                                          8. ?
9. △ABC ~ △AYX                                                   9. SAS similarity theorem

 The statement and reason missing in the proof are ∠A ≅ ∠A; reflexive property
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.

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.

Answer 2

Answer:

∠A ≅ ∠A; reflexive property

Step-by-step explanation: