question 1 - read the proof.
given: m∠h = 30°, m∠j = 50°, m∠p = 50°, m∠n = 100°
prove: △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
which reason is missing in step 2?
a)cpctc
b)definition of supplementary angles
c)triangle parts relationship theorem
d)triangle angle sum theorem

question 2-
△abc is an isosceles triangle with legs ab and ac.
△ayx is also an isosceles triangle with legs ay and ax.
the proof that △abc ~ △ayx is shown.
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
which statement and reason are missing in the proof?
a)∠a ≅ ∠a; reflexive property
b)∠x ≅ ∠x; reflexive property
c)∠abc ≅ ∠ayx; corresponding angles of similar triangles
d)∠abc ≅ ∠axy; corresponding angles of similar triangles

question 3 - line rs intersects triangle bcd at two points and is parallel to segment dc.
which statements are correct? check all that apply.
a)△bcd is similar to △bsr.
b)br/rd = bs/sc
c)if the ratio of br to bd is , then it is possible that bs = 6 and bc = 3.
d)(br)(sc) = (rd)(bs)
e)br/rs = bs/sc

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.