## Engage NY Eureka Math Geometry Module 1 Lesson 34 Answer Key

### Eureka Math Geometry Module 1 Lesson 34 Review Exercise Answer Key

Review Exercise:

Answer:

### Eureka Math Geometry Module 1 Lesson 34 Problem Set Answer Key

Use any of the assumptions, facts, and/or properties presented in the tables above to find x and/or y in each figure below. Justify your solutions.

Question 1.

Find the perimeter of parallelogram ABCD. Justify your solution.

Answer:

100, 15 = x + 4, x = 11

Question 2.

AC = 34

AB = 26

BD = 28

Given parallelogram ABCD, find the perimeter of CED. Justify your solution.

Answer:

57

CE = \(\frac{1}{2}\)AC; CE = 17

CD = AB; CE = 26

ED = \(\frac{1}{2}\)BD; ED = 14

Perimeter = 17 + 26 + 14 = 57

Question 3.

XY = 12

XZ = 20

ZY = 24

F, G, and H are midpoints of the sides on which they are located. Find the perimeter of FGH. Justify your solution.

Answer:

28

The midsegment is half the length of the side of the triangle it is parallel to.

Question 4.

ABCD is a parallelogram with AE = CF. Prove that DEBF is a parallelogram.

Answer:

AE = CF – Given

AD = BC – Property of a parallelogram

mâˆ DAE = mâˆ BCF – If parallel lines are cut by a transversal, then alternate interior angles are equal in measure.

âˆ†ADE â‰… âˆ†CBF – SAS

DE = BF – Corresponding sides of congruent triangles are congruent.

AB = DC – Property of a parallelogram

mâˆ BAE = mâˆ DCF – If parallel lines are cut by a transversal, then alternate interior angles are equal in measure.

âˆ†BAE â‰… âˆ†DCF – SAS

BE = DF – Corresponding sides of congruent triangles are congruent.

âˆ´ ABCD is a parallelogram. – If both sets of opposite sides of a quadrilateral are equal in length, then the quadrilateral is a parallelogram.

Question 5.

C is the centroid of RST. RC = 16. CL = 10. TJ = 21

SC = __

TC = __

KC = __

Answer:

SC = 20

TC = 14

KC = 8

### Eureka Math Geometry Module 1 Lesson 34 Exit Ticket Answer Key

Question 1.

The inner parallelogram in the figure is formed from the midsegments of the four triangles created by the outer parallelogramâ€™s diagonals. The lengths of the smaller and larger midsegments are as indicated. If the perimeter of the outer parallelogram is 40, find the value of x.

Answer:

x = 4