/5. D is the midpoint of side BC of triangle ABC and the bisectors of angles ADB and ADC meet AB and AC at E and F respectively. Prove: EF is parallel to BC. (See Theo- rem 54.) AutoSave Exercises 4_15 proofs 1 and. . Marc Skwarczynski ON Exercise 4.15 #3: A triangle ABC is inscribed in a circle. M is the midpoint of AMČ and BM intersects AC at D. File Home Insert Draw Design Layout References Mailings Review View Help Table Design Layout 1D Exercises 4.15 #3 Given: Inscribed AABC; M midpoint of AMC; BM intersects AC in D AB AD Prove: %3D BC DC AB Prove: BC AD Statements Reasons DC 1. (see above) 1. Given 2. CM = AM 2. Def. of midpoint 3. ZCBM = - CM; 3. An inscribed angle = ½ the intercepted arc. %3D %3D ZABM = AM M. 4. - CM = - AM 4. Division (of step 2) %3D 2. 5. Substitution 5. ZCBM = LABM %3D (step 3 -> step 4) 6. Def. of bisector 6. BM bisects ZABC 7. The bisector of an interior angle of a divides the oppos internally into se which have the sa AB 7. BC AD %3D DC as the other two 257 words fecus

Question

Theorem 54=If a line divides two sides of a triangle proportionally, then it is parallel to the third side. 

Please answer in a two-column proof-statements and reasons.
**Also, it should have ONLY one given (statement).** I have an example of how it should look like/how it should be done in the second picture.

It is about lines proportional. The question is in the picture. *The question is completely clear, so please don't reject the question.*

*Maybe, if you could, please use some of these reasons to prove the statements true. (Those below are the reasons  for the statements if you want to use)*

Definition of ~ triangles

Definition of bisector

Definition of perimeter

Definition of median

Definition of midpoint

Multiplication

Division

If 4 quantities are in proportion, then like powers are in proportion.

Subtraction Transformation

Alternation Transformation

Pythagorean Theorem

If 2 angles have their sides perpendicular, right side to right side and left side to left side, the angles are equal.

In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.

Angles inscribed in the same segment or equal segments are equal.

If a line is drawn parallel to the base of a triangle, it cuts off a triangle similar to the given triangle.

Two isosceles triangles are similar if any angle of one equals the corresponding angle of the other.

C.A.S.T.E. - corresponding angles of similar triangles are equal

C.S.S.T.P. - corresponding sides of similar triangles are proportional

Theorem 53-If a line is drawn through two sides of a triangle parallel to the third side, then it divided the two sides proportionally.

Theorem 54-If a line divides two sides of a triangle proportionally, then it is parallel to the third side (Converse of Theorem 53)

Theorem 55-The bisector of an interior angle of a triangle divides the opposite side internally into segments which have the same ratio as the other two sides.

Theorem 56-The bisector of an exterior angle of a triangle divided the opposite side externally into segments which have the same ratio as the other two sides.

Theorem 57- If two triangles have the three angles of one equal respectively to the three angles of the other, then the triangles are similar

Corollary 57-1 If two angles of one triangle are equal respectively to two angles of another, then the triangles are similar. (a.a.)

Corollary 57-2 Two right triangles are similar if an acute angle of one is equal to an acute angle of the other.

Theorem 58-If two triangles have two pairs of sides proportional and the included angles equal respectively, then the two triangles are similar. (s.a.s.)

Corollary 58-1 If the legs of one right triangle are proportional to the legs of another, the triangles are similar. (l.l.)

Theorem 59- If two triangles have their sides respectively proportional, then the triangles are similar. (s.s.s.)

Theorem 60- If two parallels are cut by three or more transversals passing through a common point, then the corresponding segments of the parallels are proportional.

Theorem 61-If in a right triangle the perpendicular is drawn from the vertex of the right angle to the hypotenuse

Corollary 61-1 If a perpendicular is dropped from any point on a circle upon a diameter, then the perpendicular is the mean proportional between the segments of the diameter.

Theorem 62-The square of the hypotenuse of a right triangle is equal to the sum of the squares of the legs.

Corollary 62-1 The difference of the square of the hypotenuse and the square of one leg equals the square of the other leg.

/5. D is the midpoint of side BC of triangle
ABC and the bisectors of angles ADB
and ADC meet AB and AC at E and F
respectively.
Prove: EF is parallel to BC. (See Theo-
rem 54.)
View transcribed image text
Expand
AutoSave
Exercises 4_15 proofs 1 and. .
Marc Skwarczynski
ON
Exercise 4.15 #3: A triangle ABC
is inscribed in a circle. M is the
midpoint of AMČ and BM
intersects AC at D.
File
Home
Insert
Draw
Design
Layout
References
Mailings
Review
View
Help
Table Design
Layout
1D
Exercises 4.15 #3
Given: Inscribed AABC; M midpoint of AMC; BM
intersects AC in D
AB AD
Prove:
%3D
BC
DC
AB
Prove:
BC
AD
Statements
Reasons
DC
1. (see above)
1. Given
2. CM = AM
2. Def. of midpoint
3. ZCBM = - CM;
3. An inscribed angle = ½
the intercepted arc.
%3D
%3D
ZABM =
AM
M.
4. - CM = - AM
4. Division (of step 2)
%3D
2.
5. Substitution
5. ZCBM = LABM
%3D
(step 3 -> step 4)
6. Def. of bisector
6. BM bisects ZABC
7. The bisector of an
interior angle of a
divides the oppos
internally into se
which have the sa
AB
7.
BC
AD
%3D
DC
as the other two
257 words
fecus
View transcribed image text
Expand

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Geometry

Triangles

Related Geometry Q&A

Find answers to questions asked by students like you.

Q: The hypotenuse of an isosceles right triangle is 6 feet long. What is the length of one leg?

A: Click to see the answer

Q: Express answers as radicals and fractions if applicable. The problem is according to Theorem 64. If ...

A: Click to see the answer

Q: Given the probability that "she's up all night 'til the sun" OR "she's up all night for good fun" is...

A: Click to see the answer

Q: Construct a right triangle having only whole number side lengths whose hypotenuse measures 26 inches...

A: Given: A right triangle having only whole-number side lengths whose hypotenuse measures 26 inches. ...

Q: Answer 14

A: Click to see the answer

Q: help!

A: Click to see the answer

Q: The length of the diagonal of a square is 12 cm, find the perimeter and area of the square.

A: Please see the picture below: S is the side of the square. It's diagonal is S√2

Q: Suppose the area of the base of a pyramid is 112 ft2 and its lateral surface area is 198 ft2. What i...

A: Given, Area of the base of the pyramid = 112 square feet Lateral surface area of the pyramid = 198 s...

Q: need help solving this

A: Click to see the answer

Q: A pasta box has dimensions of 6 x 4 x 3 inches.  If each measurement is reduced by ½ inch, how much ...

A: Click to see the answer

Q: A car is 415 centimeters long. How long is it in feet and inches? Use the fact that 1 inch = 2.54 ce...

A: Click to see the answer

Q: Question 121

A: x is the integer greater than 35 and the three sides of the triangle are 19, 21, and x.

Q: The QUESTION 15 Using Heron's Formula, calculate the area of a triangle with side lengths of 5, 7 an...

A: Heron's formula for the area of a typical triangle is shown below: We will abbreviate centimeters a...

Q: What is the standard deviation of the following: 34, 46, 16, 49, 44, 15 Round to 2 decimal places as...

A: Given set is:

Q: A farmer has a fence that encloses a square plot with an area of 49 square meters. If the farmer use...

A: Click to see the answer

Q: A rectangular garden measures 40 feet by 30 feet. It is bordered and surrounded by a path measuring ...

A: Click to see the answer

Q: Each exterior angle of a regular polygon has the measure 8°. How many sides does the polygon have? 2...

A: The formula for  measuring the  exterior angle  of a regular polygon, where n is the number of sides...

Q: HW Sco 2.2.31 Decide whether or not the equation has a circle as its graph. If it does, give the cen...

A: Click to see the answer

Q: 8. One liter of water is in a cylindrical container. The water is poured into a second cylindrical c...

A: Let R1 be the radius and H1 be the water level in the first cylindrical container and R2 and H2 be r...

Q: Find the volume of the figure, when s = 7 cm and h = 6 cm. cm3

A: We have two figures in the given figure. One is cube other is a square-based pyramid.  Cube has each...

Q: The volume of a cube is 3375 ft³. What is the length of a side of the cube? ft

A: Let the length of a side of the cube= x ft So,  

Q: Two similar polygons have perimeters in the ratio 3:5. Find the side in the second polygon conrespon...

A: Click to see the answer

Q: Find the x and y intercepts of the line that passes through the given points (4,1) and (2,2)

A: Click to see the answer

Q: About proof (statements and reasons)-similar triangles. The question is in the picture. **The questi...

A: sketch the situation roughly Given: F, K, E are midpoints of AP, PB, PC respectively. Prove:  

Q: A painter to cover a triangular region 62 meters by 66 meters by 74 meters. A can of paint covers 70...

A: Click to see the answer

Q: Solve the triangle MNO in Figure... (MN, NO,<O)

A: Click to see the answer

Q: need help solving this

A: Click to see the answer

Q: Given RM=RN=3x+4 ST=7x-1 Angle R=60 degree Find x, RM and ST.

A: Click to see the answer

Q: Write a slope-intercept form equation for the coordinates. (1,3) and (0,1)

A: Click to see the answer

Q: Number 27

A: Click to see the answer

Q: Exercises: 1) Let G = (Z6,O) .Show which of the following subsets of G is a subgroup of it? a) H = {...

A: Hey, since there are multiple questions posted, we will answer first question. If you want any speci...

Q: A Practice Another Version - Google Chrome webassign.net/v4cgi/student/practice.tpl?struct=DEaCUDhBr...

A: Click to see the answer

Q: About proofs. Please help finish the blanks. *Maybe you will have to use some of these theorems to p...

A: Click to see the answer

Q: Find the value of x. 3. a. 1.1 b. C. 7.5 d. 10

A: The side splitter theorem states that if a line is parallel to a side of a triangle and the line int...

Q: Which proportion is true for this figure? (The three horizontal lines are parallel.) a. AG BH %3D DH...

A: To Determine: Which proportion is true of this figure.                                      

Q: About proof (statements and reasons)-similar triangles. The question is in the picture. **The questi...

A: We sketch the situation roughly  Given: C is the midpoint of arc ACB AB and CP cuts at E Prove:  

Q: A spinner is broken into sections labeled 1 to 31. What is the probability that on your next spin, t...

A: Click to see the answer

Q: The floor plan of a loft that will be getting a new wood floor. How many square feet of flooring wil...

A: Click to see the answer

Q: Find the perimeter of quadrilateral ABCD

A: Click to see the answer

Q: Please finish the proof by filling it in. Maybe you will need these to prove the statement true...ac...

A: Click to see the answer

Q: Awebassign.net/v4cgi/student/practice.tpl?struct=zUDPCOCoEeAEEgCqAGDKDREUCpESAnEpDpCCDcALDhEdAqEkCXC...

A: Click to see the answer

Transcribed Image Text

/5. D is the midpoint of side BC of triangle ABC and the bisectors of angles ADB and ADC meet AB and AC at E and F respectively. Prove: EF is parallel to BC. (See Theo- rem 54.)

AutoSave Exercises 4_15 proofs 1 and. . Marc Skwarczynski ON Exercise 4.15 #3: A triangle ABC is inscribed in a circle. M is the midpoint of AMČ and BM intersects AC at D. File Home Insert Draw Design Layout References Mailings Review View Help Table Design Layout 1D Exercises 4.15 #3 Given: Inscribed AABC; M midpoint of AMC; BM intersects AC in D AB AD Prove: %3D BC DC AB Prove: BC AD Statements Reasons DC 1. (see above) 1. Given 2. CM = AM 2. Def. of midpoint 3. ZCBM = - CM; 3. An inscribed angle = ½ the intercepted arc. %3D %3D ZABM = AM M. 4. - CM = - AM 4. Division (of step 2) %3D 2. 5. Substitution 5. ZCBM = LABM %3D (step 3 -> step 4) 6. Def. of bisector 6. BM bisects ZABC 7. The bisector of an interior angle of a divides the oppos internally into se which have the sa AB 7. BC AD %3D DC as the other two 257 words fecus