Triangle Proportionality and Midsegments: Practice Level 1 | Geometry

Level 1 · Foundational 0 / 12 answered

Question 1 of 12

1

In nondegenerate triangle $ABC$ , $D$ lies between $A,B$ , $E$ between $A,C$ , and $DE\parallel BC$ . Which part-to-part equality follows?

Answer choices for question 1 A $\frac{AD}{AB}=\frac{AE}{EC}$ B $\frac{AD}{DB}=\frac{AE}{EC}$ C $\frac{AD}{DB}=\frac{AC}{AE}$ D $\frac{DB}{AD}=\frac{AE}{EC}$
2

If $AD:DB=2:9$ , what fraction of the whole side $AB$ is $AD$ ?

Answer choices for question 2 A $\frac29$ B $\frac9{11}$ C $\frac{11}{2}$ D $\frac2{11}$
3

For the ordinary side-splitter converse in a nondegenerate triangle ABC with $AD/DB=AE/EC$ , which point-location condition is required?

Answer choices for question 3 A Both division points lie inside the named sides B The triangle must be equilateral C Both parts on each side must be equal D The transversals must be perpendicular
4

A segment joins the midpoints of two sides of a triangle. Which pair of conclusions is guaranteed?

Answer choices for question 4 A It is perpendicular to the third side and equally long B It is parallel to the third side and twice as long C It is parallel to the third side and half as long D Only its length is known
5

A triangle has third side length $38$ cm. What is the length of the midsegment parallel to it?

Answer choices for question 5 A $38\text{ cm}$ B $19\text{ cm}$ C $76\text{ cm}$ D $18\text{ cm}$
6

D,E,F are the midpoints of $AB,AC,BC$ respectively. Which ordered statement always gives the natural central-to-outer matching?

Answer choices for question 6 A $\triangle DEF\sim\triangle CBA$ B $\triangle DEF\sim\triangle ABC$ C $\triangle DEF\sim\triangle BCA$ D $\triangle DEF\sim\triangle CAB$
7

Three parallel cross-lines meet transversals in corresponding order $A,B,C$ and $P,Q,R$ . Which equality follows?

Answer choices for question 7 A $\frac{AB}{BC}=\frac{QR}{PQ}$ B $\frac{AB}{AC}=\frac{PQ}{QR}$ C $\frac{BC}{AB}=\frac{PQ}{PR}$ D $\frac{AB}{BC}=\frac{PQ}{QR}$
8

Why must the compass opening stay fixed when marking equal auxiliary steps?

Answer choices for question 8 A The auxiliary ray must become perpendicular B The given segment AB must have that same length C A fixed opening guarantees equal step lengths D It makes the last point coincide with B
9

A construction marks nine equal auxiliary steps and joins the last point to B. The parallel through step 4 meets AB at X. What is AX:XB?

Answer choices for question 9 A $4:5$ B $4:9$ C $5:4$ D $9:4$
10

Which tools are enough for the exact segment-division construction taught here?

Answer choices for question 10 A A marked ruler is necessary to divide the length numerically B A protractor is necessary for every auxiliary step C A compass and an unmarked straightedge D A calculator must supply a decimal division point
11

A parallel to BC through the midpoint D of AB meets AC at E in a nondegenerate triangle. What follows?

Answer choices for question 11 A E must be the midpoint of BC B E is the midpoint of AC C AE equals the whole AB D DE must equal BC
12

To construct a ratio from two supplied positive segment lengths a and b, what is copied consecutively on the auxiliary ray?

Answer choices for question 12 A Two unrelated arbitrary compass openings B The quotient a/b as a measured decimal C Only the shorter of the two segments D AU equal to a, then UV equal to b