Answer:
49 cm, 15 cm, 45 cm, bc, 75 degrees
Step-by-step explanation:
1) Triangle ABC and LMN are similar so their angles and sides share a ratio with the other triangle. Due to similarity, AB is similar to LM. AB is 5 cm and LM is 35 cm. Because the triangles are similar, all sides must share a common ratio. 35 is 5 x 7 so LMN is 7 times larger then ABC. This expresses back into line LN which corresponds to AC. AC is 7 cm and so LN is 7 x 7 = 49 cm.
2) It can quickly be observed that DC and AB are twice that of HG and EF. Therefore trapezoid EFGH is half that of ABCD. BC is 30 cm and because it is established that trapezoid EFGH is half of ABCD, GF is BC/2 = 15 cm.
3) The same method can be used in finding this problem as the one previous. Trapezoid ABCD is thrice EFGH so AD is 3 x EH. EH = 15 so AD is 3 x 15 = 45 cm.
4) Due to laws of cross-multiplication and certain situations, ad=bc. Thankfully here these requisetes are met and the property holds true. Basically, its bc because of memorizing the property.
5) All triangles are 180 degrees. And if triangle ABC is similar to triangle XYZ then angle A = angle X, angle B = angle Y, and angle C = angle Z. From the problem we know that angle A is 45 degrees and angle C is 60 degrees. Due to the previoius statement, angle X is 45 degrees and angle Z is 60. To find angle Y all we need to do is subtract 180 degrees by the two other angles. 180 - 60 - 45 = 75 degrees.
