Suppose NP is congruent to OM and MN is congruent to PO. Can you use the SSS Postulate or the SAS Postulate to prove
2 answers:
Answer: BY SSS only
Step-by-step explanation:
In the given picture , we have two triangles ΔMNP and ΔPOM
Given : In ΔMNP and ΔPQM
Also, [By Reflexive property]
Therefore , by SSS congruence postulate , we have
ΔMNP ≅ ΔPOM
- SSS congruence postulate says that if three sides of one triangle are congruent to three sides of another triangle then the two triangles are congruent.
We can not use SAS congruence postulate because there is no information given regarding angles.
You might be interested in
For the given triangle, x = 5.1 cm and y = 6.1 cm.
Step-by-step explanation:
Step 1:
In the given triangle, the angle is 50°. It is given that the opposite side has a length of y cm and the adjacent side has a length of y cm. The hypotenuse of the triangle measures 8 cm.
To determine the length of the opposite side of the triangle, we use the sin of the given angle.
To determine the length of the adjacent side of the triangle, we use the cos of the given angle.
Step 2:
In the given triangle,
The length of the opposite side = y cm,
The length of the adjacent side = x cm,
The length of the hypotenuse = 8 cm,
The angle of the triangle = 50°.
So x = 5.1416 cm and y = 6.128 cm. Rounding these off to one decimal place, we get x = 5.1 cm and y = 6.1 cm.
Answer:
- <u>300 cheese and 900 yogurt</u>
Explanation:
<u>1. Name the variables: </u>
<u />
- C = number of units of cheese
- Y = number of units of yogurt
<u>2. State the constraints (inequalities)</u>
a) Company can make 1,200 units of product each week:
- C + Y ≤ 1,200
b) Company must produce at least 300 units of cheese,
- C ≥ 300
c) Company must produce at least 450 units of yogurt.
- Y ≥ 450
<u />
<u>3. Build the graph</u>
a) C + Y ≤ 1,200
i) Draw the line C + Y = 1,200
- Use the y-intercept (0, 1200) and the x-intercept (1200,0)
- Use a solid line because thepoints on the line are part of the solution
ii) Shade the region below the line (again the line is inclueded)
b) C ≥ 300
i) Draw a solid vertical line that passes through (300,0)
ii) Shade the region to the right of the line (the line is included)
c) Y ≥ 450
i) Draw a solid horizontal line that passes through (450, 0)
ii) Shade the region above the line (the line is included)
The solution region is delimited by those three lines and it is shown on the graph attached.
<u>4. Determine the vertices of the triangle that forms the solution region</u>
a) Intersection of the lines C + Y = 1,200 and C = 300
- Y = 1,200 - 300 = 900
- Point (300, 900)
b) Intersection of the lines C + Y = 1200 and Y = 450
- C = 1,200 - 450 = 750
- Point (750, 450)
c) Intersection fo the lines C = 300 and Y = 450
- Point (350, 450)
<u />
<u>5. Determine the profits with the three vertices</u>
The profit equation is P = $60C + $90Y
a) Point (300, 900)
- P = $60(300) + $90(900) = $99,000
b) Point (750, 450)
- P = $60(750) + $90(450) = $85,500
c) Point (300, 450)
- P = $60(300) + $90(450) = $58,500
The maximum profit is when the company produces 300 units of cheese and 900 units of yogurt.
Step-by-step explanation:
so this is the answer for the problem for you
