Let ABC be a right triangle and H be the foot of the altitude relative to the hypotenuse BC. Let also I1 and I2 be the incenters of triangles ABH and ACH. Prove that A is the excenter of triangle I1HI2 relative to I1I2

Q: Consider the triangle ΔABC and denote by P the point on the segment BC such that 4PC=BC. Suppose…

A: Consider the triangle ΔABC and denote by P the point on the segment BC such that 4PC=BC. Suppose…

Q: In the adjacent figure, ABC is a right triangle at A, such that: AB = (V17 – 1) and AC = 2V5 D (V17…

A: This question contains 4 subparts. So, according to the guidelines, the solutions of three subparts…

Q: Let AB = a and BC = b. Point M is the midpoint of BC. If AN = (AB), find the length of NM in terms…

A: Given:                  Length of AB= a,                  Length of BC=b;   Point M is the mid-point…

Q: In the diagram of AABC below, points D and E are on sides AB and CB respectively, such that DE AC.…

A: In △ABC,point D and E are on sides AB and CB respectively,such that DE∥AC       If EB is 3 more…

Q: 6. In ADEF, mLD = 50, and an exterior angle with vertex F has measure 120. What is the longest side…

A: Given that : In ∆DEF, m∠D=50, an exterior angle of vertex F has measure 120

Q: Given: BA = ED Cis the midpoint of AE and BD Prove: AABC AEDC

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Q: 6. The median to the base of an isosceles triangle is the perpendicular bisector of the base.…

A: Due to Bartleby guidelines, only 1question can be solved. Please repost the remaining questions to…

Q: 7) Given: Parallelogram ABCD with diagonals AC and BD intersecting at E. sement Iheason Prove: AADE…

A: Given a parallelogram ABCD with diagonals AC and BD intersecting at E.

Q: The side AB in the triangle ABC is greater than AC, and D is the mid-point of BC. From C draw two…

A: Given- The side AB in the triangle ABC is greater than AC, and D is the mid-point of BC. From C draw…

Q: 7.In the following figure, (LF) is parallel fto BC, prove that the triangle FHC is isosceles A F L H

A: It is given that LF is parallel to BC. And ∠AFL and ∠LFH are equal (given )

Q: 6) B is the midpoint of segment AC. AB 10x-1 and BC = 5x+ 14. Find BC. I

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Q: ABC is a right angled triangle right angled at B. If P and Q are the mid - points of the sides AB…

A: Given:

Q: Find a formula for the area of the triangle whose vertices are 0, v, , and v2 in R?. Choose the…

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Q: Let ABC be an equilateral triangle. Let M be the midpoint of BC and let N be the midpoint of AM.A…

A: Given that, ABC is an equilateral triangle and M is the midpoint of BC¯ and N is midpoint of  AM¯.…

Q: In triangle FIX, TT'is the perpendicular bisector of FX. Prove that the two triangles formed by the…

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Q: 11. ABCD is a quadrilateral such that if sides AB and CD are extended they will meet at a right…

A: Solution: Consider the given quadrilateral ABCD and assuming line AB and CD extended and create a…

Q: If any Point o inside eR ouside a tetrahedron ABCD is Joined to the Vertices and AO BO, Co ,DO are…

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Q: P and Q are the midpoints of AI and IR, respectively. Use the properties of midsegments to find the…

A: It is given that, P and Q are the midpoints of AI and IR,respectively.By using the properties of…

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A: Given △ABC Let X be any point in the plane so that AX, BX, CX are cevians of △ABC given to prove…

Q: What information is missing from HL theorem? 3. What additional information can be used to prove the…

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Q: Show that the sum of the two perpendiculars drawn from any point in the base of an isosceles…

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Q: In the adjoining figure, O is the centre of a circle. Two equal chords AB and CD intersect at P. If…

A: Given: In the above figure, O is the center of the circle and AB and CD are two equal chords…

Q: Let ABC be a right triangle and H be the foot of the altitude relative to the hypotenuse BC. Let…

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Q: 2. Consider a square ABCD and an equilateral triangle BCE in its exterior. Let F be the midpoint of…

A: We have to proof as given in the question.

Q: Which two triangles are congruent by the SAS Theorem? Complete the congruend statement. R RST E DBC…

A: We have to check

Q: GIVEN AE = CE, AB = CD, E is the midpoint of BD. PROVE AEAB = AECD C A. %23 E B.

A: Plan :  We know that, if the three sides of two triangles are congruent then the triangles are…

Q: . If M is the midpoint of the hypotenuse AB of right triangle ABC, andAM = 6, find MB and MC.

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Q: Show that the two triangles are similar. Q P and ZN Z Nv, so ALvQ AMNP QLN QNL MPN MNP NMP

A: Two triangles △LNW and △MNP are shown in the figure given in the problem. From the figure, LQ||MP…

Q: If any point D is taken on the base BC of an isosceles triangle ABC and DEF is drawn perpendicular…

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Q: S and E are the midpoints of BA and AM, respectively. Use the properties of midsegments to find the…

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Q: In a triangle XYZ, which is right angled at Y, find the side length of YZ, if XY = 5 cm and zC = 30°…

A: Given: XY=5 cm ∠C=30°

Q: In the diagram, ACDE is a cyclic quadrilateral, Lines GAB and FEHC are paraliel, and line GAB is a…

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Q: Show that the two triangles are similar. Q P and ZN INV, so ALNQ AMNP. QLN QNL MPN MNP NMP IN

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Q: In the accompanying diagram of a right triangle ACD, B lies on AC, BD is drawn such that m2CDB = 27,…

A: Solve the following

Q: 7. Let ABCD be a trapezoid with bases lengths BC = b and AD = a. Assume the diagonal of ABCD…

A: Consider the given information, Let ABCD be a trapezoid with bases Bc=b and AD=a. The diagonals of…

Q: Find the value of x that would prove this is an isosceles trapezoid. Then find each segment length.…

A: x=8.   the explanation is given in below step

Q: Given the isosceles triangle ABC with AB=AC=x and BC=2y.   show that if A s the area of the…

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Q: Let a and b be lengths of legs and let c be the length of the hypotenuse of a right triangle. Prove…

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Q: AWXY and AABC are isosceles, with bases WY and AB respectively. If ZX and ZB are each 50° and WX =…

A: Given, Isosceles triangle WXY and ABC. WY and AB are bases Angle X= Angle B= 50° WX=BC

Q: 3.) AWXY and AABC are isosceles, with bases WY and AB respectively. If ZX and ZB are each 50° and WX…

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Q: 7.) Find the area of the triangle ABC under the given conditions: a) A = 44°, b = 3 ft, and c = 2 ft…

A: Here I have provided solution with formulas in step 2.

Q: Given: MT and HA intersect at B, (MA)(HT) and MT bisects HA Prove: MT = HA Part A: Annotate the…

A: Given : MT and HA intersect at BMA || HT and Mt bisect HAto prove : MT = HAIn ∆MAB and ∆ HBT

Q: Show that the two triangles are similar. Q P v and ZN so ALNQ AMNP.

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Q: In AABC, AD I BC. Prove that AB > AD; AB > BD. Thus, in a right triangle, the hypotenuse is the…

A: In triangle ABD, we gave,  AB² = AD² + BD²

Q: Given: LBAC LBCA, M and N are midpoints of AB and CB, respectively Show: LAMC LCNA M.

A: Given  ∠BAC≅∠BCA M and N are midpoints of AB and CB , this implies  AM=MBCN=NB To show: ∠AMC≅ ∠CNA…

Q: Use the diagram shown to prove the Pythagorean Theorem a² + b = c A D B C

A: The solution for the above question is as shown below.

Q: ABC is a right-angled triangle at A. Show that, if AD is the per- pendicular from A to the…

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Q: 3. Label each triangle as acute, obtuse, right angle, isosceles, equilateral, and scalene. AAA 80…

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Q: Given: E is the midpoint of AB and CD Prove: ΔΑEC - ΔΒED C

A: Given that: E is the mid point of AB and CD