Prove that if two triangles have congruent bases, then their areas are in the same ratio as their heights.

Q: 5.1. 5.1.1. State whether True or False. If you say False, then justify: Let OR be the positively…

A: (5.1.1)  Answer :  TRUE Explanation:  Green's theorem:  Let C be a positively oriented piecewise ,…

Q: Let AD and BE be the altitudes of the congruent sides of an isosceles triangle ABC and F its…

A: Let AD and BE be the altitudes of the congruent sides of an isosceles triangle ABC and F its…

Q: A rhombus can be divided by its diagonals into four 3-4-5 right triangles. What is its area?

A: To find the area of rhombus

Q: Prove: The diagonals of a rectangle intersect to form four congruent segments.

A: Given: Rectangle ABCD. To prove: Diagonals of a rectangle intersect to form four congruent segments.

Q: Prop. 43: For every parallelogram, the complements of the parallelograms about the diameter are…

A:

Q: Use the following theorem to construct a triangle similar to the given triangle but with sides that…

A: We need to construct a similar triangle to the given triangle so that the sides should be in…

Q: It is given that  AC = BD. After proving that △BAD≅△ABC△BAD≅△ABC  and △ADC≅△BCD△ADC≅△BCD, a teacher…

A: Given step by step clear explanation

Q: 4. Points A(xA , YA), B(xB,YB), and C(xc,Yc) form a triangle AABC. Let D, E, and F be midpoints of…

A: Using coordinate system we can prove two triangles are similar using distance formula. If length of…

Q: Find the length of h, the height drawn to the hypotenuse, of the right AABC with right angle at C if…

A: We can find the answer as below.

Q: there is no /BAC LEDF, AB DE, and BC EF, but AC DF.

A: Given that: The Two triangle △ABC and △ DEF. Where ∠BAC ≅ ∠EDF , AB¯ ≅ DE¯ , and BC¯ ≅ EF¯ , but AC¯…

Q: 3) Which equation can be used to find A, the area of the parallelogram shown? 7 cm 10 cm A A = ¹ × 7…

A:

Q: (a) Define what it means for two triangles AABC and ADEF to be congruent. (b) State the SAS…

A:

Q: Prove that the diagonals of a parallelogram bisect each other.

A:

Q: Use the converse of Ceva’s theorem to prove that the angle bisectors of the interior angles of a…

A:

Q: (5) Prove that in an Isosceles triangle, the angle bisector at the apex angle is also the median and…

A:

Q: Prove that parallelogram of the same base and the same parallel lines are equal in area.

A: Given: parallelogram of the same base and the same parallel lines are equal in area.To prove: Area…

Q: 1. State and prove the full version of the Pythagorean Theorem

A:

Q: 2. It is possible for two angles of a triangle in the hyperbolic plane to each have a measure of 2.

A: Solution

Q: Prove that an exterior angle of a regular polygon is equal to the angle at the center?

A: Let us consider a regular n-polygon  We know that the sum of the exterior angles of a polygon is =…

Q: prove: two isosceles triangles are similar if and only if their angles at the vertex are congruent

A:

Q: Suppose AABC is a triangle in the Euclidean plane and D is the point such that B*C*D and AD bisects…

A: Given:  AB=9AC=6CD=12 B*C*D means points B, C, Dare distinct and they lie on the same line.  B*C*D…

Q: A cyclic quadrilateral ABCD is inscribed in a circle whose sides AB-10cm, BC-20cm, CD-30cm and…

A: By Ptolemy's theorem,  We know that, in a cyclic quadrilateral, the sum of product of the two pairs…

Q: (4) Prove that if two altitudes in a triangle are congruent, then the triangle is Isosceles.

A:

Q: AJAM is a right triangle. a. Is JM an altitude of AJAM? b. Name another altitude shown. c. In what…

A: Since you have posted multiple subparts, as per our policy we will answer first three subparts.…

Q: Which two triangles are congruent by the SAS Theorem? Complete the congruence statement. E

A: Consider

Q: 10. Use the Pythagoras theorem to find the missing lengths of the following triangles. The theorem…

A:

Q: AB²+ AC² = 2(AO² + BO²) e O is the middle point of BC.

A: Part A

Q: In any obtuse triangle, the square of the side oppo- site vne obtuse angle is equal to the sum of…

A:

Q: Are the triangles congruent by the HL Theorem? A

A:

Q: Prove that a quadrilateral can be inscribed in a circle if and only if its opposite angles are…

A:

Q: D с B

A:

Q: prove that if one side of a triangle is a common measure of the other two sides then the triangle is…

A:

Q: Prove that if a triangle has two congruent angles, then it is isosceles.

A: Triangle with two equal sides is called anisoceles triangle.To prove: If a triangle has two…