High School Statutory Authority:
Carefully trace the triangle below onto tracing paper. Be sure to copy the angle markings as well. Then rotate the triangle to make a shape that looks like a parallelogram. Is your new shape truly a parallelogram? Use the angles to convince your teammates that the opposite sides must be parallel.
Then write a convincing argument. What else can the congruent triangles tell you about a parallelogram? Look for any relationships you can find between the angles and sides of a parallelogram. Does this work for all parallelograms? That is, does the diagonal of a parallelogram always split the shape into two congruent triangles?
Refer to the parallelogram below. Knowing only that the opposite sides of a parallelogram are parallel, create a flowchart to show that the triangles are congruent. What shape did he make?
Jan 19, · 1. Write an indirect proof to show that opposite angles of a parallelogram are congruent. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted. 2. Triangle ABC is congruent to triangle DEF. In triangle ABC, side AB measures 13, side BC measures x+13, and side CA measures Status: Resolved. Write a formal proof using the two-column, paragraph, or flow chart format. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. (aka an indirect proof). 2 credits. No partial credit will be allowed. For each question, write on the triangles to prove that it’s opposite sides are congruent. L M O N A B. 8 GEOMETRY Test 1 The Terry Fencing Company has been asked to give an estimate for the cost of enclosing a.
What transformation s did Kip use to form his shape? What do the congruent triangles tell you about the angles of this shape? KITES Kip shared his findings about his kite with his teammate, Carla, who wants to learn more about the diagonals of a kite.
Carla quickly sketched the kite at right onto her paper with a diagonal showing the two congruent triangles. Trace this diagram onto tracing paper and carefully add the other diagonal. Then, with your team, consider how the diagonals may be related. Use tracing paper to help you explore the relationships between the diagonals.
If you make an observation you think is true, move on to part b and write a conjecture. If you have not already done so, write a conjecture based on your observations in part a. When she drew the second diagonal, Carla noticed that four new triangles appeared.
Now extend your proof from part c to prove your conjecture from part b.Opposite sides of a parallelogram are parallel. Opposite sides of a parallelogram are congruent. lso assesses MAD Use methods of direct and indirect proof and determine. whether.
a short proof is logically valid. MAG Write. If an indirect proof is used to prove the following theorem, then which assumption must be A quadrilateral with both pairs of opposite sides congruent.
b. A quadrilateral with the diagonals bisecting each other. d. Quadrilateral with two opposite sides parallel. In the following polygon, determine the value of x. a. 78 b. 81 c.
95 d. Write a paragraph proof. Text Book, Calculator, Notes Postulate, Theorem Homework, Use indirect proof to show that the triangles are congruent. Text Book, Calculator, Notes Indirect Proof, properties of the sides and angles of the parallelogram.
Find the . Write equiangular, Angles opposite congruent sides of a triangle are congruent. 3) Transitive Property of Congruence Theorem If a quadrilateral is a parallelogram, then its opposite sides are congruent.
Theorem If a quadrilateral is a parallelogram, then . Centerville Jr.
High School Curriculum Mapping. Geometry. 1st Nine Weeks. Matthew Lung.
Unit/ Chapter/ Lesson indirect proof to show that the triangles are congruent. Text Book, Calculator, Notes properties of the sides and angles of the parallelogram. Find the missing side lengths and angle measures in the. triangles prove or show that triangles are congruent.
Use theorems about the angles of a triangle Use SAS, SSS, HL, ASA and AAS to prove Indirect proof is an alternate way of explaining or reasoning. Midsegment Theorem and the Triangle Inequality Theorem.
Write indirect proofs. Use dynamic geometry software to visualize and represent.