Drag and drop a statement or reason to each box to complete the proof. statement reason △abc , de⎯⎯⎯⎯⎯∥ac⎯⎯⎯⎯⎯ given corresponding angles postulate △bde∼△bac babd=bcbe polygon similarity postulate ba=bd+dabc=be+ec bd+dabd=be+ecbe substitution property of equality bdbd+dabd=bebe+ecbe addition of fractions 1+dabd=1+ecbe simplify. dabd=ecbe subtraction property of equality

1. Definition of median , 2. QM≅RM , 3. PM≅PM, 4. SSS Congruence Postulate  and 5. CPCTC.

Step-by-step explanation:

The given information is  PQ≅PR.

Draw a median PM,

In triangle PQM and PRM,

Statement                                          Reason

PQ≅PR                                                 (Given)

QM≅RM                                               (M is Median)

PM≅PM                                                (Reflextion property)

By SSS Congruence Postulate

∠Q≅∠R                                                                (CPCTC)

Therefore the required solutions for the blanks are

1. Definition of median ,

2. QM≅RM

3. PM≅PM

4. SSS Congruence Postulate

5. CPCTC

1. EF≅HG

2. EF║HG

3. Definition of parallelogram

4. when two parallel lines are cut by a transversal, alternate interior angles are congruent

5. EK≅GK

   FK≅HK

Step-by-step explanation:

1. As per the properties of a parallelogram, the opposite sides are congruent.

hence in given parallelogram EFGH the two sides EF≅HG

2. As per the properties of a parallelogram, the opposite sides are parallel.

hence in given parallelogram EFGH the two sides EF║HG

3.  Definition of parallelogram: A quadrilateral is called a parallelogram if two of its opposite sides are parallel.

4. As per the properties of transversal lines, when two parallel lines are cut by a transversal, alternate interior angles are congruent.

5. As proven in given question ΔEKF≅ΔGKH, so as per the CPCTC

                      EK≅GK and FK≅HK

!

1. MN≅QP

  MQ≅NP

2. MP≅MP

3. SSS congruence postulate

4. ∠N≅∠Q

5. CPCTC

Step-by-step explanation:

1. As per the property of parallelogram that opposite sides are congruent, in given case of parallelogram MNPQ the opposite sides

                    MN≅QP  and   MQ≅NP.

2. The reflexive property of congruence states that a line or a geometrical figure is reflection of itself and is congruent to itself. Hence in given case of parallelogram MNPQ

                                         MP≅MP

3. SSS congruence postulate stands for Side-Side-Side congruence postulate, it states that when three adjacent sides of two triangle are congruent then the two triangles are congruent. In given case of parallelogram MNPQ, as the sides MN≅Q, MQ≅NP and MP≅MP hence

                               ΔMQP≅ΔPNM

5. As proven in part 4 that ΔMQP is congruent to ΔPNM, so as per the property of CPCTC (congruent parts of congruent triangles are congruent)

                                 ∠N≅∠Q

5. CPCTC stands for congruent parts of congruent triangles are congruent.

!

definition of midpoint

Reflexive property of congruence

SSS congruence postulate

CPCTC theorem

Step-by-step explanation:

Step 1: Since, M is the midpoint of the line segment QR.  

 definition of midpoint

Step 2: The reflexive property of congruence states that a line segment or an angle or a shape is always equal to itself.  

Reflexive property of congruence.

Step 3: The SSS congruence postulate states that if three sides of a triangle are equal to three sides of another triangle, then the two triangles are congruent.

 SSS congruence postulate

Step 4: CPCTC theorem states if two triangles are congruent then the sides and angles are also congruent.

CPCTC theorem.

Given below is completed proof

Step-by-step explanation:

Given PQ=PR

Statement                                   Reason

PQ≅PR                                          Given

Point M is the midpoint of QR¯¯¯¯

Draw median PM¯¯¯¯¯¯ .Two points determine a line.

PM=PM                             Reflexive Property of Congruence

QM=RM                             Definition of midpoint  

△PQM≅△PRM             SSS axiom(side, side, side)

∠Q≅∠R                              Congruence property for triangles

Hence proved

hope this helps :)

your question helped me and so ill help you

hope this helps :)

your question helped me and so ill help you

The data observed from the triangle are given below.

Statement                         Reason

                         Given

Draw so that M is the midpoint of QR.     Two points determine a line

                         Definition of midpoint

                        Reflexive property of congruence

               SSS congruence postulate

                       CPCTC

SSS means side-side-side

CPCTC means corresponding parts of the congruence triangle are congruent.

Hence the given triangle is SSS congruence postulate

The proof is explained below.

Step-by-step explanation:

Given a triangle PQR in which PQ=PR.

We have to prove that  ∠Q≅∠R

We prove this by two methods, in a simple way if in triangle two sides are equal then it becomes an isosceles triangle. In triangle PQR sides PQ and PR are equal i.e PQ=PR then PQR becomes an isosceles triangle.

which implies its two base angles are equal gives ∠Q≅∠R

Now, By Congruency postulate,

It is given that draw a line segment PM such that M bisect the line QR i.e M is the mid-point of QR.

In ΔPQM and ΔPRM,

PQ=QR       (Given)

QM=MR       (Given)

PM=PM        (Common)

It gives all the sides equal. Hence, by SSS Postulate, which states that if three sides of two triangles are congruent then these two triangles are congruent.

∴ ΔPQM≅ΔPRM

By CPCT, ∠Q≅∠R

The question is incomplete. The complete question has been added as an attachment to the solution.

To aid easy identification of the unknowns, I attached another document where I numbered the unknowns.

1) EF ≅ HG

2) EF || HG

3)

4) When two parallel lines are cut by a transversal, alternate interior angles are congruent.

5) EK ≅ GK

FK ≅ HK

Step-by-step explanation:

1) In the given parallelogram EFGH,

It is stated that the opposite sides of a parallelogram are congruent. Therefore, EF ≅ HG

2) It would be noted from the properties of a parallelogram, that the opposite sides are parallel. Therefore, EF || HG

3) Definition of a parallelogram: A parallelogram is a quadrilateral with two opposite sides that are parallel and equal in length.

4) One of the properties of a parallelogram states that when two parallel lines are cut by a transversal, alternate interior angles are congruent.

5) It can be seen from the question that △EKF≅△GKH as a result of congruence Postulate.

And the CPCTC proves,

EK ≅ GK

FK ≅ HK

CPCTC means Corresponding Parts of Congruent Triangles are Congruent.

When you have two triangles that have been proven as congruent, then each part of one triangle is equal in size and shape to the corresponding part in the other triangle.