SocialTwist Tell-a-Friend

Ask a Question? Get an Answer!


Question: State the property of congruence and name the congruent triangles from the figure shown.



A ) SAS, ΔACB @ ΔACD
B ) SSS, ΔACB @ ΔACD
C ) ASA, ΔACB @ ΔACD

Steps to derive

2 From the figure, ∠BAC ≅ ∠DAC, ∠ACB ≅ ∠ACD and the included side AC is common for both triangles.

3 According to the ASA congruence property, ΔACB ≅ ΔACD.



Hence the right answer is Option C

Click Here To Go Back


Few Other Questions -

  • CD and GH are angular bisectors of ∠ACB and ∠FGE and ΔABC ∼ ΔFEG. ..
  • ABCD is a parallelogram FD‾ || AB‾, ∠BAE = 50o, ∠CFB = 54o. Find ..
  • D is a point on side BC of ΔABC such that m∠ADC = m∠BAC. If CA = 20 cm and C..
  • If RMMS = 38 , then find Area of ΔPRQ Area of ΔPQS...
  • In the figure, AB‾ || DE‾. AC = 4 cm, CE = 6 cm and DB = 15 cm. Find BC&Ov..
  • Which of the following statements are true about similarity?..
  • Which of the following are true for two similar triangles?I. Corresponding sides are propo..
  • The measures of the sides of ΔABC are, AB = 6 cm, BC = 8 cm and CA = 13 cm. What sha..
  • Which theorem can prove ΔABC and ΔDEF similar?..
  • If ABDE = ACDF = BCEF, then which theorem can prove that ΔABC is similar to Δ..
  • ABDE = ACDF, by which of the following, can ΔABC be proved to be similar to ΔD..
  • The measures of two angles of ΔABC are 35 and 63. What shall be the measures of th..
  • ΔABC is similar to ΔPQR. AB = 12 cm, BC = 13 cm and AC = 10 cm. If PQ = 5 cm, ..
  • Similar triangles have..
  • Which of the following is true?..
  • Select the correct statements.I. All right triangles are always similar.II. Similarity is..
  • ΔPQR is similar to ΔABC. If PQ = 3 in., PR = 5 in., and AB = 8 in., then find ..
  • If two figures have the same area, then they are always..
  • If two triangles are similar, then they are always..
  • Find the value of k if the line ky = (k - 1)x + 3k is parallel to y = 2x + 5...
  • What is the slope of a line parallel to 4x + 3y + 7 = 0? ..
  • The lines 20x - 4y + 9 = 0 and y = 5x + 11 are..
  • In a plane, two lines parallel to a third line are..
  • In a plane, two lines perpendicular to a third line are..
  • The slopes of non-vertical parallel lines are ..
  • Identify the correct statement.I. Vertical lines are perpendicular to each other.II. Verti..
  • A(1, - 3), B(5, 4), C(3, 2), D(2, 0) are the coordinates of 4 points in the x - y plane. I..
  • Which of the following lines is parallel to x = 3?..
  • Slope of a line parallel to 2x + 3y + 6 = 0 is..
  • A(4.5, 5), B(2, 5), C(1.5, - 2), D(3, - 2) are the coordinates of 4 points in the x-y plan..
  • What is the slope of a line parallel to y = 3?..
  • The lines x = 3 and x = 7 are..
  • Which of the following is not parallel to y = (35)x + 6?..
  • Find the equation of a line parallel to x = 3 and passing through (4, 5)...
  • Find the equation of the line parallel to y = 4 and passing through (6, 5). ..
  • Find the equation of the line parallel to y = 2x + 3 and passing through (1, 2)...
  • A line AB↔ makes an angle of 60o with the positive x-axis. What is the slope of any l..
  • What is the inclination of a line parallel to y = x - 3 ?..
  • If the line through (3, y) and (2, 7) is parallel to the line through (- 1, 4) and (0, 6),..
  • Choose the equation of the line passing through the point (- 5, 1) and parallel to the li..
  • What is the value of p if the lines y = 3x + 7 and 2y + px = 3 are parallel to each other..
  • What is the slope of a line parallel to y-axis?..
  • What is the slope of a line parallel to x-axis?..
  • Number of lines parallel to a line and passing through a given point is/are..
  • Find the product of the slopes of x-axis and y-axis...
  • For a given surface area, which of the following has the least volume?..
  • For a given volume, which of the following will have the maximum surface area?..
  • If the radius of a sphere increases by 30%, then the new surface area will be..
  • If a solid sphere of radius r is cut into two equal parts, then what will be the change in..
  • If a sphere of radius r is cut into two parts, then the change in volume is..
  • A plane that intersects a sphere is 10.5 in. from the center of the sphere. If the radius ..
  • The total surface area of a hemisphere of radius r is..
  • Volume of the hemisphere of radius r is..
  • A sphere of radius r is melted and made into a hemisphere. The radius of hemisphere formed..
  • Six parallel lines are intersected by two lines. How many triangles can be formed?..
  • There are 9 parallel lines. The distance between the first 5 consecutive lines is 2 cm eac..
  • How many lines parallel to a given line can be drawn through a given point out side the li..
  • If two lines are perpendicular to the same line in a plane, then the lines are..
  • How many lines perpendicular to a given line can be drawn through a given point outside th..
  • In a plane, if two lines are parallel to a third line, then they are..
  • Are parallel lines useful in finding angle measures in triangles?..
  • ABCD is a trapezoid. Find the value of x...
  • What is m∠ADE, if DE‾ || BC‾?..
  • ED || AB; Find m∠EDC. [Given x = 70 and y = 60]..
  • ABCD is a parallelogram. Find m∠DAB...
  • Prove that m∠ACB = 50 using the properties of parallel lines...
  • If line l || line m and b = 120, then find the value of y...
  • Two plane mirrors r and s are parallel to each other. If m∠ABK = 30, then find m∠D..
  • What is the most appropriate description for the figure ABCD if ∠A = ∠B ?..
  • What is the most appropriate name for the figure ABCD if ∠ B = ∠ D and AB = BC?..
  • How many perpendicular lines can be drawn from a fixed point to 5 lines which are paralle..
  • Two right triangles are placed such that one of its legs is horizontal. How many pairs of..
  • Choose the line which is inclined to 4y + 7x + 13 = 0. ..
  • Are BA‾ and CE‾ parallel?..
  • Identify the correct statement / statements.1. Lines lying on different planes can be para..
  • The number of points of intersection of two perpendicular lines is..
  • A line is parallel to its image under reflection by a mirror. The angle at which the line ..
  • Find the number of regions into which two parallel lines divide a plane...
  • Identify the correct statement.I. Perpendicular lines have same slope.II. Perpendicular li..
  • What is the slope of a line perpendicular to 2x + 3y + 9 = 0?..
  • What can you say about the lines 3x + 2y + 5 = 0 and 2x - 3y + 7 = 0?..
  • If the line through (x, 3) and (4, 9) is perpendicular to the line through (- 1, 4) and (3..
  • What is the product of the slopes of two perpendicular lines, neither of which is vertical..
  • What is the product of the slopes of the lines x = 7 and y = 7?..
  • Identify the correct statement.I. The coordinate axes are perpendicular to each otherII. T..
  • Which of the following lines are perpendicular to x = 3?..
  • What is the slope of the line perpendicular to 2x + 3y + 6 = 0?..
  • A (- 3, 2), B (5, 1), C (2, 7), D (1, - 1) are the coordinates of 4 points in the x-y plan..
  • What is the slope of a line perpendicular to y = 4?..
  • The lines x = 3 and y = 3 are..
  • Which of the following is not perpendicular to y = 2x + 6?..
  • What is the equation of the line perpendicular to x = 5 and passing through (4, 6)?..
  • What is the equation of the line perpendicular to y = 2 and passing through (2, 4)?..
  • What is the equation of the line perpendicular to 2x + y + 3 = 0 and passing through (0, ..
  • A line AB makes an angle of 60o with the positive x-axis. What is the slope of any line pe..
  • Find the inclination of a line perpendicular to y = x - 3...
  • If the line through (3, y) and (2, 7) is perpendicular to the line through (- 1, 4) and (0..
  • What is the equation of the line through the point P (- 5, 1) and perpendicular to the lin..
  • Find the value of p, if the lines y = 3x + 7 and 2y + px = 3 are perpendicular to each ot..
  • Find the slope of a line perpendicular to y-axis...
    		•