Name: Unit 1 Test Study Guide
(Geometry Basics)
Date:
Per:
M
Topic 1: Points, Lines & Planes
Use the diagram to the right to answer questions 1-4.
1. Name two points collinear to point K.
2. Give another name for line b.
3. Name the intersection of line c and plane R.
4. Name a point non-coplanar plane R.
H
b
Use the diagram to the right to answer questions 5-8.
5. How many planes are shown in the figure
6. Give another name for plane W.
7. Name the intersection of plane ADE and plane W.
8. Name a point non-collinear to points A and B.
A
Oy
Topic 2: Segment Addition Postulate
9. If DF = 42, find DE.
7x + 1 4x-3
10. In the diagram below, if JL = 10x - 2.
JK = 5x - 8, and KL = 7x - 12. find KL.

I’m going to infer you said parallel.solve for yy= -1/2x+7/4lines that are parallel have the same slope, different y intercept.so we know m is -1/2then from there solve for y intercept.

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

4y - 6 + y^2 - 9 = y^2 + 4y - 15y^2 term terms- termstotal of 3 terms when simplified

Prove that every odd prime number can be written as a difference of two squares.prove also that this presentation is unique.is such presentation possible if p is just an odd natural number? can 2 be represented this way?

answers

\3. yes the presentation (i.e. odd numbers being written as differences of two squares) is possible for all odd natural number however the presentation may not be unique. for example,  57=112−82=292−28257=112−82=292−282.

\4. 2 can't be written as a difference of two squares because 4-1=3 and 1-1=0 and the difference of squares grows to integers larger that 3.

can i get some in proving questions 1 and 2?