1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Bumek [7]
3 years ago
12

Two isosceles triangles share the same base. Prove that the medians to this base are collinear. (There are two cases in this pro

blem: vertices are on the same side of the base and vertices are on the opposite sides of the base!)

Mathematics
1 answer:
Anna71 [15]3 years ago
3 0

Answer:

Given: Two Isosceles triangle ABC and Δ PBC having same base BC. AD is the median of Δ ABC and PD is the median of Δ PBC.

To prove: Point A,D,P are collinear.

Proof:

→Case 1.  When vertices A and P are opposite side of Base BC.

In Δ ABD and Δ ACD

AB= AC   [Given]

AD is common.

BD=DC  [median of a triangle divides the side in two equal parts]

Δ ABD ≅Δ ACD [SSS]

∠1=∠2 [CPCT].........................(1)

Similarly, Δ PBD ≅ Δ PCD [By SSS]

 ∠ 3 = ∠4 [CPCT].................(2)

But,  ∠1+∠2+ ∠ 3 + ∠4 =360° [At a point angle formed is 360°]

2 ∠2 + 2∠ 4=360° [using (1) and (2)]

∠2 + ∠ 4=180°

But ,∠2 and ∠ 4 forms a linear pair i.e Point D is common point of intersection of median AD and PD of ΔABC and ΔPBC respectively.

So, point A, D, P lies on a line.

CASE 2.

When ΔABC and ΔPBC lie on same side of Base BC.

In ΔPBD and ΔPCD

PB=PC[given]

PD is common.

BD =DC [Median of a triangle divides the side in two equal parts]

ΔPBD ≅ ΔPCD  [SSS]

∠PDB=∠PDC [CPCT]

Similarly, By proving ΔADB≅ΔADC we will get,  ∠ADB=∠ADC[CPCT]

As PD and AD are medians to same base BC of ΔPBC and ΔABC.

∴ P,A,D lie on a line i.e they are collinear.




You might be interested in
What equation do I need to use?
goldenfox [79]
To ease your problem, consider "L" as you x-axis
Then the coordinate become:
A(- 4 , 3)   and B(1 , 2) [you notice that just the y's changed]

This is a reflection problem.
Reflect point B across the river line "L" to get B', symmetric of B about L.
The coordinates of B'(1 , -1) [remember L is our new x-axis]
JOIN A to B' . AB' intersect L, say in H
We have to find the shortest way such  that AH + HB = shortest.
But HB = HB' (symmetry about L) , then I can write instead of 
AH + HB →→ AH + HB'. This is the shortest since the shortest distance between 2 points is the straight line and H is the point requiered 


6 0
3 years ago
Instructions: Determine whether the following polygons are
sergiy2304 [10]

Answer:

None

Step-by-step explanation:

The given angles aren't equal which is needed for the polygon to be similar

7 0
2 years ago
Cesar danced for 16 minutes on Saturday. On Sunday he danced for 28 minutes more than he did on Saturday. How long has he danced
KIM [24]

Answer:

60 minutes

Step-by-step explanation:

Saturday = 16 minutes

Sunday = 28 minutes + 16 minutes = 44 minutes

Saturday + Sunday = 44 + 16 = 60 minutes

3 0
1 year ago
PLEASE HELP KINGSSSS
creativ13 [48]

Answer:

30/52

Step-by-step explanation:

its a 26/52% chance to get a black card because 13 spain cards and 13 clovers add it together you get 26 and theirs 4 kings in a dack so add them both together 26/52+4/52=30/52

<h2>Answer: 30/52</h2>
3 0
2 years ago
1 fourth to the 3rd power as a fraction
lukranit [14]
1/64 is the answer as a fraction
7 0
2 years ago
Read 2 more answers
Other questions:
  • I need to solve these problems. Plz solve theses problems ASAP.
    8·2 answers
  • Order 7\8,0.98, 8/9 from least to greatest
    5·1 answer
  • Find the quotient.<br> 36s^3t-26st<br> -----------------<br> -2st<br> Enter the correct answer.
    6·1 answer
  • Sam has 2 brothers. His brothers are 5 cm shorter and 7 cm shorter than him. Sam's height is 140 cm. What is the median height o
    13·1 answer
  • during the first play of a football game, you lose 3 yards. you gain 7 yards during the second play. what is your total gain of
    9·2 answers
  • Find g(1) if g(x) = x^2 + 1.<br> 2 3
    9·1 answer
  • Example 3: Seven sheets of coloured paper are on Shannon's desk. If there are four sheets
    11·1 answer
  • For each diagram below, write and solve an equation.
    15·1 answer
  • PLEASE HELP ME MATH IS HARD
    15·2 answers
  • (It is reborn) I'm totally chill 'bout this question but please help <br> From- <br> xXIndieKidXx
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!