Solution)
In triangles
CDF and BDE
We have
Angle DCF= angle DBE (isosceles triangle)
Angle CFD= angle BED (90° as lines are perpendicular)
CD= BD (mid point segments)
Thus triangle CDF is similar to triangle BDE (A.A.S axiom of congruency)
Thus
FD= ED (corresponding sides of congruent triangles)
Which is required to prove hence proved.
A 5. GIVEN: AABC is isosceles D is the midpoint of BC FDI AC DE 1...
4. The following figure shows triangle AABC with side lengths AB = 10, BC = 8, and CA = 5. DE is constructed to be parallel to AB and to originate at point D, the midpoint of AC. C X10 D Ε B A Write the lengths for the segments listed below. BE = ED= DA=
Need 14 and 16 14. The point D on the hypotenuse BC of the right isosceles AABC is such that BD= AB. Prove that ZBAD = 67.5° baAB = CD, then AD | BC 16 Prove that the sum of the interior angles of a quadrilateral is 360° ADCD tho hieectors of the interior onel
C 1 7. [8] AABC and ADEB are both right triangles. AC = 3 AB = 4 Also, D is the midpoint of AB. Find DE E A B D
Additional problem 1 Let AABC be a triangle, let be the bisector of the angle ZCAB Let P be the intersection of and BC. Let R be the point on the line AB such that AR-AC, and let X-APnRC. Let Q denote the intersection point between the line through B and X and AC. (a) Show that the triangle AARC is isosceles, and deduce that RX-XC. (b) Apply Menelaus's theorem to the triangle AARC with the line through B, X,...
3 nat you ho has cheated on this exam. 1. Let AABN and AA'B'Y by asymptotic triangles. Prove that if LABN 2 ZA'B'Y and AB> ΑΒ , then /BAΩ< ΒA. 2. Let AABC be an ordinary triangle and let D be any point of the interior. Prove that the sum of the angles of AABD is greater than the sum of the angles of AABC. 3. Suppose that two lines & and m have a common perpendicular MN. Let A...
Additional Problem: Suppose that AABC has sides AB 31,AC 35, and M is the midpoint of BC. The goal is to obtain the inequality 2 < x <33, where x AM. Construct the auxiliary lines shown, with M the midpoint of AE a. Find y-CE. Then show that 2x-AE 66. b. Show that AM (66)-33 C. Show that 2 < x < 33. (Hint: Use the Triangle Inequality in AEC. 31 35
Kindly answer the question neatly. Thanks. In AABC, AB = AC and BC = 6 cm. D is a point on the side AC such that AD = 5 cm and CD = 4 cm. Show that ABCD – AACB and hence find BD.
ABIBC=AC E PEPEDED b) In the figure below, AACB and A DAB are isosceles, with AC = BC, and AD AB. IF ZACB = 50° and ZDAG = 45°, find all other angles and mark them in the figure. Show all your work. С ДАСВ D <CABY <ABC 2. CCABALACB=1880 . sop 26 CAB = 180-50 CAB = 65° - LABC A B
1. Consider the isosceles triangle ABC, with AB = AC, and BAC = 20. Choose points E, D on the sides AB, AC, respectively, so that ZCBD = 60', and BCE = 50'. We will find LEDB. (i) Bring the parallel DF to BC, with F on AB. Connect points and F. and let K be the intersection of BD and CF. Show that DFBC is an isosceles trapezium. Mark all its angles. (ii) What type of triangles are BKC...
can you please please help me with these proofs R Cand CoDNder the triangle AABC and M and NIwopaints such thatM PrOve that MEMAN kBA) M MBC)m ACRI. Let AABC be a triangle with AB< AC and let D be a point such that A C - D. Show that for every point M with B- M- C we have m(< ABM) +m(< BMA)> m(< CMD)+m(< MDC) Prove that if in the triangle AABC the altitudes AD and BE (where...