Question: Using congruency of triangles, prove that diagonals of a parallelogram bisect each other.
Steps to derive
1 Figure:
2 From parallelogram ABCD,
3 ∠ABD ≅ ∠CDB
4 ∠DCA ≅ ∠CAB
[Alternate angles are equal.]
5 AB‾ ≅ CD‾ & AB‾ || CD‾
6 AD‾ ≅ BC‾ & AD‾ || BC‾
7 Hence ΔOAB ≅ ΔOCD
[ASA postulate.]
8 Since the two triangles are congruent, OB‾ ≅ OD‾ & OA‾ ≅ OC‾
9 So, O is the midpoint of diagonals BD & AC. Hence, diagonals of a parallelogram bisect each other.
Hence the right answer is Option
Click Here To Go Back
Few Other Questions -
Solve: 4t - 3 + 32t = -4t + 37..Find the range of the data shown in the line plot...A group of students in 10th grade went on a botanical trip. On the way back from the trip,..There are some t-shirts and a few number of shoes in the figure. Write the ratio of shoes ..The weights(in pounds) of 6 different wagons are 1284, 1284, 1852, 716, 1852 and 2136. Fin..There are some t-shirts and a few number of shoes in the figure shown below. Write the rat..There are some t-shirts and a few number of shoes in the figure. What is the ratio of shoe..The weights (in pounds) of 6 different carts are 1288, 1288, 1864, 712, 1864 and 2152. Fin..The serving speed (miles per hour) of some of the tennis players who participated in a ten..There are some t-shirts and some caps. Write the ratio to represent a comparison of caps t..The scatter plot displays the weight of Brian as he grew old. What was his weight when he ..There are some t-shirts and some caps in the picture. Write the ratio of caps to the whole..The scatter plot displays the weight of Josh as he grew old. At what age was his weight 50..A wholesale dealer of stationery products plots the scatter diagram of his income through ..There are some t-shirts and some caps in the picture. Write the ratio of t-shirts to whol..There are some fruits in the picture. What is the ratio of bananas to pineapples?..The scatter plot displays the income earned by a wholesale dealer of stationery products t..There are some fruits in the picture. What is the ratio of watermelons to whole group?..Henry won 4 out of 7 matches he played. Identify the ratio of the matches lost to the matc..Solve: 10p + 10 + 4p = 4p + 8..The prices of different chocolates sold in a store are $6, $5, $6, $4, $10, $6, $15, $10 ..The table shows the results of a survey in which students were asked whether they worked p..The prices of different sweets sold in a store are $10, $9, $10, $8, $18, $10, $27, $18, a..What is the number n, if n is subracted from 8 is n more than 16?..A classroom has 56 chairs and 14 tables. Find the unit rate of chairs per table...Tony's score in five matches are 23, 17, 26, 29, and 20. Find Tony's average score...The sum of 10 less than a number and the number itself is three times the number. Find the..Six less than the product of a number n and 3 is equal to the product of the number n and ..George's score in five tests are 22, 18, 24, 26, and 20. Find the range of scores...Find the mode of the set of letters. F, C, H, F, G, K, G, K, N, K..Ed can read 48 pages in 4 hours. Find the unit rate in pages per hour...The scatter plot shows the number of hours children of different ages sleep. Find the numb..Find the mode for the data shown in the line plot...Find the median for the data set, which shows the scores of 10 students in Edward's class...The weights (in pounds) of 10 students in Mr. Edward's class are 63, 58, 62, 59, 64, 65, 6..The scatter plot shows the number of vehicle transactions in different quarters of the yea..Which would be a better buy, 5 sharpeners for $2.75 or 7 sharpeners for $3.50?..The weights (in pounds) of 10 students in Mr. Edward's class are 60, 55, 59, 56, 61, 62, 6..The stem and leaf plot shows the scores of eleven teams in a tournament. What is the mean..The stem and leaf plot shows the scores of eleven teams in a tournament. What is the rang..The number of doctors in a state during the last 4 decades is given in the table. Determi..The number of students in a city during the last 4 decades is given in the table. What is..The ratio of male members to female members in a golf club is 4 : 3. Find the number of ..Find the mode for the data shown in the line plot...The stem and leaf plot shows the number of burgers sold at a bakery over a fortnight. Find..Edward can blow 24 balloons in 4 hours. How many balloons can he blow in 6 hours?..The stem and leaf plot shows the number of burgers sold at a bakery over a fortnight. Find..The stem and leaf plot shows the number of burgers sold at a bakery over a fortnight. Find..Find the median of the data set, which shows the heights (in inches) of 10 students in Mr...The scores of 10 students in Jim's class are 62, 57, 61, 58, 63, 64, 64, 64, 59 and 74. Fi..The stem and leaf plot shows the scores of eleven teams in a tournament. What is the mean..The stem and leaf plot shows the scores of eleven teams in a tournament. What is the rang..7 pens cost $22 in a supermarket. Find the cost of 56 such pens...The cost of 3 cakes is $7. Find the cost of 9 cakes...An Opera house charges $5.50 per person as an entry ticket. If a family paid $38.50 for th..Paul can walk a distance of 9 km in 4 hours. How much time would he take to cover a dist..What is the ratio of the consumption of goods in 1997 to that in 1999 as found in the scat..The scatter plot represents the distance traveled by Paul at different speeds. How many mo..The table shows the prices for different sizes of shower gel packs. Which size has the low..Identify the unit rate of primavera sauce, if 4 liters cost $12...The scatter plot shows the times taken by Rose to reach City B from City A at different sp..The cost of 6 yards of ribbon is $1.32. Find the unit rate of ribbon...There are 13 tables for 39 chairs. How many chairs are needed if there are 143 tables?..A parking ticket costs $7 for 4 hours. How many hours did George park his car, if he paid ..Katie drives at a constant speed from Orlando to Chicago. The scatter plot shows the dista..A dogwood tree can grow 0.6 meters in 1 year. How many meters will it grow in 7 years?..The scatter plot shows the population of Alabama and California from 1998 through 2002. By..The population of a village in the last 4 decades is given in the table. Determine the ra..The number of doctors in a town during the last 4 decades are given in the table. Find the..Find the mode for the data shown in the line plot...The scatter plot shows the population of Alabama and California from 1998 through 2002. By..The scatter plot displays the weight of Sunny as he grew older. What was his weight when h..The scatter plot displays the weight of Victor as he grew in age. At what age was his weig..A wholesale dealer of stationery products plots the following scatter diagram of his incom..The scatter plot displays the income earned by a wholesale dealer of stationery products f..The scatter diagram shows the yield of an apple orchard. Find the increase in the number o..What is the ratio of the consumption of goods in 2000 to that in 1998 as seen in the scatt..A secretary receives 44 phone calls in 12 hours. How many phone calls do you think she mig..Find the median of the data set, which shows the heights (in inches) of 10 students in Mr...The weights (in pounds) of 10 students in Mr. Tommy's class are 67, 62, 66, 63, 68, 69, 69..The scores of 10 students in Mr. Anderson's class are 61, 56, 60, 57, 62, 63, 63, 63, 58 a..Find the mean of the data set.12, 41, 17, 53, 63, 19, 45, 122, 31, 42..Find the outlier of the data set.48, 117, 55, 128, 138, 59, 121, 206, 59, 107, 118. Find t..The length of a ladder in a picture is 4 inches. The scale of the picture was 1 inch : 13..The table shows the heights of the students in Mr. Francis's class. Find the median of the..The scatter plot shows the number of soft ball matches won by a team from 1986 to 1990. Fi..The table shows the heights of the students in Mr. Arthur's class. Find the range of the d..The table shows the average rainfall in a city during 5 months. What is the mean rainfall ..The scatter plot shows the number of matches won by teams representing the USA from 1986 t..The table shows the average relative humidity in a town during 5 months. Find the range of..The table shows the heights (in inches) of the students in Mr.Trowell's class. Find the me..The table shows the heights of the students in Mr. Jacob's class. Find the range of the da..The table shows the average monthly rainfall in a village in the last 5 months. Find the r..The scatter plot shows the number of teachers hired each year from 1980 through 1984. How ..A die-cast model of a sail boat was prepared using a scale 1 inch: 0.4 meters. If the mode..The scatter plot shows the number of students and the number of hours they work each day. ..How many times will the volume of a rectangular prism increase, if its length, width and h..The scatter plot shows the number of students and the number of hours they work everyday. ..Simplify: 73 - 44 + 3..Evaluate the expression n2 - n4 for n = 2...
|
|
